SOLUTION: find x, if; {{{ (5+2sqrt2)^(x^2-x) + (5-2sqrt2)^(x^2-x) =10 }}}

Question 753630: find x, if;

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Consider the function

is the sum of two exponential functions,
with positive bases, .
Those two exponmential functions, and , increase with throughout their real numbers domain, from -infinity to infinity.

So for -->
and for -->
The only value of that makes is

Then, the only solutions for
will be the solutions of

-->
Applying the quadratic formula, we find
-->

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