MathsEconomics:


There are actually two choices for t. t=±7
Here's a recurrence relation to use to confirm this.

Darivie04:
Nice little problem.

MathsEconomics:

I suppose the x's are digit in the "base a" representation of the A's, right?

Darivie04:
Nice little problem.

Silentscreamer:
Help me solve this.
fit the equation y=Co+C1sinpix+C2cospix to the data points (0.2,1)(0.4,2)(0.6,3)(0.8,5)(1,5)(1.2,3) using method of least squares. Co, C1 and C2 are constants.

MathsEconomics:

This is what you asked. Right?

MathsEconomics:


This is what you asked. Right?

MathsEconomics:

Here's my solution. The first part of the proof is by induction.

Darivie04:

Nice solution but in your third page can you explain what you did to turn your first inequality into the second?

By "the second" here I'm referring to the one containing (-xna^n) and (-xnb^n)

Martinez39:
Can you list the mathematics textbooks you've read and, if possible, the one's you are currently reading.

Silentscreamer:
Yes. Include the point (0.6,3).

MathsEconomics:


Hit my email or if possible scroll through my previous posts you'll find my Mobile number in one of my posts. I feel it's not going to be wise listing the Mathematics textbooks I've read in this forum.

gpercuxionz:
Solution to this please
2^x + 3^x = 13

MathsEconomics:


Alright.

Martinez39:
What stunt are you trying to pull?

gpercuxionz:
saw that in an IGCSE maths textbook under indices topic

gpercuxionz:
I will snap and send it tomorrow

gpercuxionz:
Solution to this please
2^x + 3^x = 13

Darivie04:
Nice little problem.

Darivie04:

Here's my solution.

It could be shorter but oh well I've already typed it. There might be minor typos and you'll have to zoom in a bit to see some things clearly.

MathsEconomics:


Your lemma is not true and it does not in any way relate to the preposition you're proving since n is required to be greater than unity.

Secondly. If you're proving an if and only if statement, you proof must be in two parts.
The first part is to show that the assertion is true when the given conditions are satisfied. The second part is to show that if the assertion is true. Then the given condition must be satisfied.


Moreover this problem is 1970 IMO. The solution given at the back of Topics In Algebra and Analysis is unsatisfactory.

Martinez39:
I will like to see the question.

gpercuxionz:
.

Darivie04:

You can not be kidding me ...

The whole reason I've spent about 3 week on the first chapter of that book was because I've been trying to solve every exercise and understand everything. That was supposed to be my first tough problem or problem that I felt was tough that I actually solved. If its not then I really don't know.

Seems like I'm just wasting effort trying to be good at something I might as well never be

gpercuxionz:

MathsEconomics:


For number 61. It is easy to see that x = 2 is a solution, it is also not difficult to see that this is the only solution since the function on the LHS is strictly increasing while the function on the RHS is a constant function.
It follows that these two curves can intersect in at most a single point in any coordinate system and thus our equation has only one solution which is x=2.

The remaining problems there are suitable for SS1 students. Not my cup of tea.

gpercuxionz:
Is there any workings to show that x = 2.

gpercuxionz:
Is there any workings to show that x = 2.