# how to find the solution for this inequality?

The question is $(2+\sqrt3)^{x^2-x}+(2-\sqrt3)^{x^2-x}\ge14$

how will i proceed with this question?

I'm not able to think of any idea of how to solve this question

• Try to prove the function is monotone in certain interval(may have inf. endpoint) using calculus techniques. – user175968 Jul 18 '16 at 6:03
• A graph might help. google.com/… – user175968 Jul 18 '16 at 6:03
• is it possible using rules of logarithm – danny Jul 18 '16 at 6:04

Hint: $2-\sqrt 3=\dfrac1{2+\sqrt3}$. And you should be able to proceed.
As a rule of thumb, every time you have something like $A^x+B^x=C$, you either find a trick like the one above or you have little hope for an algebraic solution.
• Solve $T+\frac1T\ge14$ for appropriate $T$. – user228113 Jul 18 '16 at 6:13