maths guru..... solve 3^x + 4^x =5^x.

afobam:
maths guru..... solve 3^x + 4^x =5^x.

Use graphical method. Mere looking gives the value of x to be 2.

yh ure right but pls can u snap and upload that

thankyouJesus:
Use graphical method. Mere looking gives the value of x to be 2.

is there any method apart from using graph

thankyouJesus:
Use graphical method. Mere looking gives the value of x to be 2.

afobam:
is there any method apart from using graph

Then you can use Binomial Expansion or better still Newton's Iterative method

.

DatechMan:

Q2

DatechMan:


Kindly write the questions on a paper and snap. The trig question is not clear

I don come again, integrate $(sin2x)^6 and integrate sin inverse.

Sin inverse of what what ? make your question clear,better still upload a photo of it.

Meel:
I don come again, integrate $(sin2x)^6 and integrate sin inverse.

Q1

Sirneij:
No one to address these?
c DatechMan
cc Richiez

Q3

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afobam:
is there any method apart from using graph

This is a classical example of limitations of analytical methods.
Note: Not all problems are solvable analytically or say easily solvable.

Bro, you need to solve that question using either Graphical method or Numerical methods.

The solution is quite trivial, graphically.

f(x) = 5^x - 4^x - 3^x

Here is an online plotter. http://rechneronline.de/function-graphs/


HAPPY NEW YEAR

#GodBlessNigeria

Sirneij:
1. Use the principle of mathematical induction to show that the arithmetic mean is always greater than or equal to the geometric mean.
2. Prove that (3 + square root5)ⁿ + (3 - square root5)ⁿ is an even integer for all natural numbers n using the principle of mathematical Induction.
3. Use the principle of Mathematical Induction to Prove that 2002^{n +2} + 2003^{2n + 1} is divisible by 4005.
4. Prove by Mathematical Induction that ¹/₂ + cosx + . . . + cos(n - 1)x = ^{sinx/2(2n - 1)}/_2sinx/2

I must mention that some of this your questions, especially 1 - 3 need not be proved using Mathematical inductions because they are self sufficient.
Meanwhile check out agentofchange1 solutions. Ask questions if you are not clear


Q1
Agent of Change has tried to adapt the proof to Mathematical Induction.


Full proofs here. Check it out

http://www.artofproblemsolving.com/wiki/index.php?title=Proofs_of_AM-GM


Q2
agentofchange1 can you tell us why you think it is you have sufficiently proved the expression when the terms in the bracket cannot be said to be integers or Rational number to say the least.
Kindly expatiate. Because 2y is always even if only y is a non-zero integer.

Thanks

yes sir , off-course 2k is always even for all non-zero k

i will post an alternative proof Asap

DatechMan:


I must mention that some of this your questions, especially 1 - 3 need not be proved using Mathematical inductions because they are self sufficient.
Meanwhile check out agentofchange1 solutions. Ask questions if you are not clear


Q1
Agent of Change has tried to adapt the proof to Mathematical Induction.


Full proofs here. Check it out

http://www.artofproblemsolving.com/wiki/index.php?title=Proofs_of_AM-GM


Q2
agentofchange1 can you tell us why you think it is you have sufficiently proved the expression when the terms in the bracket cannot be said to be integers or Rational number to say the least.
Kindly expatiate. Because 2y is always even if only y is a non-zero integer.

Thanks

Show that 3^4n+2 + 2.4^3n+1 is exactly divisible by 17 if n is a positive integer. Pls do not write snap because i'm using small phone but kindly type. Ur solution will highly be appreciated.

Orthega:
Show that 3^4n+2 + 2.4^3n+1 is exactly divisible by 17 if n is a positive integer. Pls do not write snap because i'm using small phone but kindly type. Ur solution will highly be appreciated.

my flex small,
from the question using mathematical induction,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾.
When n=1,
3^(4(1)+2) + 2.4^(3(1)+1)=1241.
The answer is divisible by 17.
Show for when n=2.
For nth term,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾.
For (n+1)th term,
3^(4(n+1)+2) + 2.4^(3(n+1)+1).
3^(4n+4+2) + 2.4^(3n+3+1).
3⁽⁴ⁿ⁺⁶⁾ + 2.4⁽³ⁿ⁺⁴⁾.
Since (n+1)th term is true for all n which is a positive integers, then,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾ is divisible by 17.

Pls help out

Timothy3113:
Pls help out

$sin^-1x dx =
$1 X sin^-1x dx.
By integration by part.
let u=sin^-1x.
sinu = x------------(1).
u' cosu = 1.
divide both sides by cosu.
u' = 1/cosu.--------(2).
Recall that sin²u + cos²u = 1.
cosu = sqrt 1 - sin²u.
from (1).
cosu = sqrt 1 - x².
into (2).
u' = 1/sqrt 1 - x².
Let dv = 1 dx.
v = x.
$udv = uv - $vdu.
You should be able to continue from here, if not, go to number 3 solution.

$x/sqrt (1-x² dx.
Let u = 1 - x².
Du/dx = 2x.
Dx = du/2x.
Substituting back into the question.
$(x/sqrt u) du/2x.
1/2$1/sqrt u du.
1/2$u^-1/2 du.
You should be able to continue from here, sorry about the rough work, my phone is not ........................

$sin⁶2x dx. $(sin²2x)³ dx. Recall that. Cos4x = cos (2x + 2x). Cos4x = cos²2x - sin²2x. Cos4x = 1 - 2sin²2x. Sin²2x = (1-cos4x)/2. You should be able to continue from here.

@Timothy, thankyouJesus has done primarily all the work, but in case you need answers to cross check:

1. xSin^-1x + √(1-x²) + c

2. ¹/₈[(5/2)x-Sin4x+(3/16)Sin8x+(1/12)Sin³4x] + c

3. -√(1-x²) + c.
I just hope I've not made any mistake

thankyouJesus:
my flex small,
from the question using mathematical induction,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾.
When n=1,
3^(4(1)+2) + 2.4^(3(1)+1)=1241.
The answer is divisible by 17.
Show for when n=2.
For nth term,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾.
For (n+1)th term,
3^(4(n+1)+2) + 2.4^(3(n+1)+1).
3^(4n+4+2) + 2.4^(3n+3+1).
3⁽⁴ⁿ⁺⁶⁾ + 2.4⁽³ⁿ⁺⁴⁾.
Since (n+1)th term is true for all n which is a positive integers, then,
3⁽⁴ⁿ⁺²⁾ + 2.4⁽³ⁿ⁺¹⁾ is divisible by 17.

Tnx bt d soln is not complete.

agentofchange1:
Q2

pls, let ur soln to be clear as that of timothy 3113. Ur kindness will highly be appreciated,tnx.

ok

Orthega:
pls, let ur soln to be clear as that of timothy 3113. Ur kindness will highly be appreciated,tnx.

gat all solutions here bt the network is too poor over here ,will upload later

you are correct bro,

GreatYinkus:
@Timothy, thankyouJesus has done primarily all the work, but in case you need answers to cross check:

1. xSin^-1x + √(1-x²) + c

2. ¹/₈[(5/2)x-Sin4x+(3/16)Sin8x+(1/12)Sin³4x] + c

3. -√(1-x²) + c.
I just hope I've not made any mistake

here,

Timothy3113:
Pls help out

Q2










Q3 ( Check (*) ) above

here

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eche45:
Have being following this thread.
But this my 1st time of posting here.
I must say u guy are doing a great job. Watch out for my own questions o. Me too will b trying to solve some issue here.
Thanks.

Yet u criticize mathematician nd compare dem to economists, why dont you use ur dumb engineering brain nd solve all ur math problem. Crystallised creatinous fvcktard