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

please help with this question

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

  • $\begingroup$ still not able to figure how to proceed $\endgroup$ – danny Jul 18 '16 at 6:10
  • $\begingroup$ Solve $T+\frac1T\ge14$ for appropriate $T$. $\endgroup$ – user228113 Jul 18 '16 at 6:13
  • $\begingroup$ :} understood.. $\endgroup$ – danny Jul 18 '16 at 6:15

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