http://familyesperience..com/2016/04/an-alternative-method-of-deriving.html

we need to encourage our youths who wish to contribute to the academic world. look at how this igbo guy proved Almighty Formula in a different way.

.

What are we suppose to do with ur picture,where are your derivation?

amiskurie:
What are we suppose to do with ur picture,where are your derivation?

brother Nawaooo!!!! u no c the link above? check the link first b4 complaining. or are u jealous about the guys breakthrough?

must u include anambra? yeebos and inferiority like bread n butter

u still have to share it with us here on nairaland so we can deliberate on it

So ??

OP, your mathematical proving is NOT different from completing the square. All those differentiation you were doing are redundant and unnecessary complications. It is simply a circumlocution for completing the square, or still, a distractor. If you compare your procedure properly with that of the conventional completing the square, the only difference is your inclusion of x(x+b/a) to both sides of the equation which is more time consuming and waste of real estate. I mean, look at equation 5. Rearrange it and compare and contrast against completing the square then you'll be able to filter out the complications that made your 'novel' procedure look as though it was different from completing the square.
Btw, equation 1 and 3 might have some issues you might want to check.
But I like people who like maths

so wu dis thread eep

BlackHummer:
OP, your mathematical proving is NOT different from completing the square. All those differentiation you were doing are redundant and unnecessary complications. It is simply a circumlocution for completing the square, or still, a distractor. If you compare your procedure properly with that of the conventional completing the square, the only difference is your inclusion of x(x+b/a) to both sides of the equation which is more time consuming and waste of real estate. I mean, look at equation 5. Rearrange it and compare and contrast against completing the square then you'll be able to filter out the complications that made your 'novel' procedure look as though it was different from completing the square.
Btw, equation 1 and 3 might have some issues you might want to check.
But I like people who like maths

OK ,lets do this little comparison.

* while you complete a square so as to have a perfect square trinomial at the LHS, which after factoring yields the binomial (X+ b/2a)^2, I differentiate a monic quadratic equation whose square - half automatically yields a binomial
(X +b/2a)^2 which is then added to the both sides of the monic quadratic for expansion, so as to cancel like terms.

so, while you factorize for completing the square principle, I expand in this method, and this is the major reason for their difference.

Also,the application of first order derivative contributes to its difference.

if you believe so,the you would believe that factoring by grouping method and box method are the same. but they are not. see, in method,once one or two steps alter,the methods are not the same again, rather similar just like the case of
Gaussian and Gauss-Jordan rule for linear systems.

As of the equations, 1 and 3, I have corrected them.

Thanks anyway.

yunglivochi:
so wu dis thread eep

it helps mathematical - minded people because, they will be happy

op I can't see what we are discussing or is it audio,you know I definitely don't like.... you know wara mean...

Pls, I need just 200 "likes" on Facebook to win a competition. And I know that you can help me to achieve that by clicking on this link:
https://m.facebook.com/story.php?story_fbid=1019111638159235&id=100001812256041

Oyiboman69:
op I can't see what we are discussing or is it audio,you know I definitely don't like.... you know wara mean...

Ahh! Brother, u are too quick to conclude. Open the link above before complaining.
That is what others do before writing comments.

"I definitely don't like......", said by you.
That I don't understand. Na u know wetin u mean

en0uwem:
Pls, I need just 200 "likes" on Facebook to win a competition. And I know that you can help me to achieve that by clicking on this link:
https://m.facebook.com/story.php?story_fbid=1019111638159235&id=100001812256041

OK I shall do mine

SlimShaddy10:
http://familyesperience..com/2016/04/an-alternative-method-of-deriving.html

we need to encourage our youths who wish to contribute to the academic world. look at how this igbo guy proved Almighty Formula in a different way.

Bro, what u just did was simply trying to show us how efficient completing the square method is... Don't think u can win an award with that.... I like ur instincts though.

SlimShaddy10:


OK ,lets do this little comparison.

* while you complete a square so as to have a perfect square trinomial at the LHS, which after factoring yields the binomial (X+ b/2a)^2, I differentiate a monic quadratic equation whose square - half automatically yields a binomial
(X +b/2a)^2 which is then added to the both sides of the monic quadratic for expansion, so as to cancel like terms.

so, while you factorize for completing the square principle, I expand in this method, and this is the major reason for their difference.

Also,the application of first order derivative contributes to its difference.

if you believe so,the you would believe that factoring by grouping method and box method are the same. but they are not. see, in method,once one or two steps alter,the methods are not the same again, rather similar just like the case of
Gaussian and Gauss-Jordan rule for linear systems.

As of the equations, 1 and 3, I have corrected them.

Thanks anyway.

Bro, what u did is still completing the square. Aside this, there are tons of issues I could raise from your opening statement to the end. I just don't feel it is needful though. But if you love maths this much and you keep pushing further, you'll hit something big by God's grace

SlimShaddy10:

it helps mathematical - minded people because, they will be happy

SlimShaddy10:

it helps mathematical - minded people because, they will be happy

buharisbae:
must u include anambra? yeebos and inferiority like bread n butter

are u sure u're not the one with the inferiority complex? If not, why the worry?

BlackHummer:

Bro, what u did is still completing the square. Aside this, there are tons of issues I could raise from your opening statement to the end. I just don't feel it is needful though. But if you love maths this much and you keep pushing further, you'll hit something big by God's grace

U still don't get it brother.
See, the method of completing a square has the name because, after taking C/a to the RHS Then we form a perfect square trinomial at the LHS which when factorized gives a perfect square binomial. It is for this reason that the method got the name,'completing the square'.

But this method did not do anything like trying to form any perfect square so as to get a perfect square binomial rather, the method uses derivative to get directly the perfect square binomial which is expanded. On this note, the method is different from method of completing the square.

Hope you construe my meaning

SlimShaddy10:


U still don't get it brother.
See, the method of completing a square has the name because, after taking C/a to the RHS Then we form a perfect square trinomial at the LHS which when factorized gives a perfect square binomial. It is for this reason that the method got the name,'completing the square'.

But this method did not do anything like trying to form any perfect square so as to get a perfect square binomial rather, the method uses derivative to get directly the perfect square binomial which is expanded. On this note, the method is different from method of completing the square.

Hope you construe my meaning

Na wah oh. You still want us to keep going backwards and forward again and again.

This is completing the square:
Xsq + bx/a = -c/a
Add to both sides the square of half the coeff of x
Xsq + bx/a + (b/2a)sq = -c/a + (b/2a)sq
Factorise
(X+b/2a)sq = -c/a + (b/2a)sq...this is completing the square....eqn(a) you are using the first derivative of the equation to complete the square!
....
....
From equation 5 in your model,
Xsq + bx/a + c/a +(x+b/2a)sq = (x +b/2a)sq ....this is still attempting to complete the square!

You now rearranged to have:
(X+b/2a)sq = (x+b/2a)sq - (xsq + bx/a + c/a)

You now expanded:
(X+b/2a)sq = xsq + bx/a + (b/2a)sq - xsq - bx/a - c/a

You now simplified:
(X+b/2a)sq = (b/2a)sq - c/a.....eqn (b)

How is eqn (a) different from (b) aside from being less complicated? All you just did is to complicate the procedure for completing the square.

Bros, trust me when I say this is nothing but beating about the bush. It won't hold water.

BlackHummer:



Na wah oh. You still want us to keep going backwards and forward again and again.

This is completing the square:
Xsq + bx/a = -c/a
Add to both sides the square of half the coeff of x
Xsq + bx/a + (b/2a)sq = -c/a + (b/2a)sq
Factorise
(X+b/2a)sq = -c/a + (b/2a)sq...this is completing the square....eqn(a) you are using the first derivative of the equation to complete the square!
....
....
From equation 5 in your model,
Xsq + bx/a + c/a +(x+b/2a)sq = (x +b/2a)sq ....this is still attempting to complete the square!

You now rearranged to have:
(X+b/2a)sq = (x+b/2a)sq - (xsq + bx/a + c/a)

You now expanded:
(X+b/2a)sq = xsq + bx/a + (b/2a)sq - xsq - bx/a - c/a

You now simplified:
(X+b/2a)sq = (b/2a)sq - c/a.....eqn (b)

How is eqn (a) different from (b) aside from being less complicated? All you just did is to complicate the procedure for completing the square.

Bros, trust me when I say this is nothing but beating about the bush. It won't hold water.

given

aX^2 + bX + C = 0

X^2 + ( b/a)X = -c/a


Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

so my guy, do u see where the name came from? the reason of completing this square is to have a quadratic equation at the LHS which would yield us the same factors ( X+b/2a)(X+b/2a) after factoring, noting that the product is (X+b/2a)^2

so, the process of getting to this point is to form a perfect square trinomial and nothing else brother ahh!
just simple thing to understand. no need to argue.

but I did not form any perfect square so as to get the same binomial (X+b/2a)^2.

well, I don't wish to argue with you again. believe me or don't. I know what I did. if you doubt me,then take this to some one who is good in maths to check it's difference.

SlimShaddy10:


given

aX^2 + bX + C = 0

X^2 + ( b/a)X = -c/a


Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

so my guy, do u see where the name came from? the reason of completing this square is to have a quadratic equation at the LHS which would yield us the same factors ( X+b/2a)(X+b/2a) after factoring, noting that the product is (X+b/2a)^2

so, the process of getting to this point is to form a perfect square trinomial and nothing else brother ahh!
just simple thing to understand. no need to argue.

but I did not form any perfect square so as to get the same binomial (X+b/2a)^2.

well, I don't wish to argue with you again. believe me or don't. I know what I did. if you doubt me,then take this to some one who is good in maths to check it's difference.

Ok

hausadreturn:
are u sure u're not the one with the inferiority complex? If not, why the worry?

Ask me ooo ooooo.!!!!!

SlimShaddy10:


OK ,lets do this little comparison.

* while you complete a square so as to have a perfect square trinomial at the LHS, which after factoring yields the binomial (X+ b/2a)^2, I differentiate a monic quadratic equation whose square - half automatically yields a binomial
(X +b/2a)^2 which is then added to the both sides of the monic quadratic for expansion, so as to cancel like terms.

so, while you factorize for completing the square principle, I expand in this method, and this is the major reason for their difference.

Also,the application of first order derivative contributes to its difference.

if you believe so,the you would believe that factoring by grouping method and box method are the same. but they are not. see, in method,once one or two steps alter,the methods are not the same again, rather similar just like the case of
Gaussian and Gauss-Jordan rule for linear systems.

As of the equations, 1 and 3, I have corrected them.

Thanks anyway.

So na even you... He you just wan showcase ursef smh

[quote author=Obas101 post=45102908]

So na even you... He you just wan showcase


guy make your self what u wanna be . no hard feelings

I just hate maths especially when they ask us to find X

Obas101:


So na even you... He you just wan showcase ursef smh

Are you jealous? if you are, good for u.

SlimShaddy10:


Are you jealous? if you are, good for u.

It's no big deal, i should be the telling good for you

Obas101:


It's no big deal, i should be the telling good for you

well, I am not the one who brought the method. it was my cousin. But I am good in mathematics also. So,b4 blogging this, I have read it over and over, and have even studied it together with a professor of maths who encouraged him (my cousin) to write it as a project for publication. So, my cousin is the one who did that, and is the one in the pix.

no hard feelings

amiskurie:
What are we suppose to do with ur picture,where are your derivation?

content of the link ..

The solutions of a quadratic equation are given
by two methods among which are : factoring
method and quadratic formula. But quadratic
formula (a.k.a, Almighty formula) as opposed to
the factoring method, works in every quadratic
equation so far as the discriminant is non
negative. Many alternative Derivations of the
quadratic formula have been given in different
texts. In this write-up, I shall show a distinct
means of deriving the Almighty formula . See
the nature of the quadratic formula in equation
1.0.
X = -b ± sqrt( b^2 - 4ac) / 2a...........1.0
At this point, instead of using the completing
the square principle for the proof, I proof it this
way.
Given a general quadratic equation of the form
aX^2 + bX + C = 0, where X is an unknown, while
a,b,and c are known numbers such that a is not
zero. Let this quadratic equation be the first
equation, i.e,
aX^2 + bX + C = 0................1
Form a monic quadratic equation by multiplying
equation one by 1 / a. This yields the second
equation i.e,
X^2 + (b/a)X + C / a = 0............2
Let F(X) = X^2 + (b/a)X + c/a = 0
Differentiate to have
F'(X) = 2X + (b/a)
Dividing the derivative by 2 and squaring the
result
gives
(F'(X)/2)^2 = ( X + b/2a)^2
Now add this square -half of the derivative to
the both sides of equation two.
Doing this we have,
X^2+(b/a)X+c/a + ( F'(X)/2)^2
= (F'(X)/2)^2...............3
But (F'(X)/2)^2 =( X + b/2a)^2
We then substitute to have
X^2 + (b/a)X + c/a + (X+b/2a)^2 =
(X +b/2a)^2................4
Isolating the LHS binomial we have ( X + b/2a )
^2 = ( X+b/2a )^2 - ( X^2 + b/aX + c/a)......5
Expanding the RHS binomial we have
( X + b/2a )^2 = X^2 + b/aX + b^2 / 4a^2 - ( X^2
+ b/aX + c/a) .......6
We cancel out like terms to have ( X + b/2a) ^2
= b^2 / 4a^2 - c/a............7
We take the LCM at the RHS to have,
( X + b/2a )^2 = b^2 - 4ac / 4a^2.............8
Take the square root of both sides to have,
X + b/2a = ±sqrt(b^2 - 4ac) / 2a.............9
Isolate X to have
X = - b/2a ± sqrt( b^2 - 4ac) / 2a..............10
We take the LCM of the RHS to have
X = - b ± sqrt( b^2 - 4ac ) / 2a..............11
Q.E.D
By
The unique nature of this method is that, it
saves us the stress of trying to complete a
square which would have led to factoring the
perfect square. Here, we only expand so as to
eliminate like terms.
Note : This write - up was made by
Makasi Chinedu on the 26 day of April 2016.