1 Attachment(s)

Equation that makes my life harder

Hello everybody.

I have an equation that I am trying to solve for 7 hours. But nothing made me success, unfortunately. So I decided to ask for help there.

Attachment 29790

I will be very lucky if somebody helps me to solve my problem.

P.S.: Sorry for my English, I am only beginner now.

Re: Equation that makes my life harder

Let x=2X

(4+sqrt(15))^X + (4-sqrt(15))^X = 8^X

An obvious solution is X=1 . So x=2.

Re: Equation that makes my life harder

Thank you for finding the solution but I have already found it.

I must proof that this equation has only one decision. (I can't proof it using graph because it is enough difficult to construct y=(4+sqrt(15))^X + (4-sqrt(15))^X without, for example, WolframAlpha).

Re: Equation that makes my life harder

Let and

so that

Multiply this equation by

since

1 Attachment(s)

Re: Equation that makes my life harder

I'm probably idiot, but I don't really know, how to solve this equation. Sorry. Attachment 29801

Re: Equation that makes my life harder

Re: Equation that makes my life harder

I don't know how to solve this equation either and I don't see how letting will help.

On the other hand if you graph the function

with

you will notice that it is decreasing and that

This shows that is the only solution

To __prove __that it is the only solution you would have to show

Re: Equation that makes my life harder

Quote:

Originally Posted by

**Idea** I don't know how to solve this equation either and I don't see how letting

will help.

On the other hand if you graph the function

with

you will notice that it is decreasing and that

This shows that

is the only solution

To

__prove __that it is the only solution you would have to show

My mistake ! You are right.