Find-the-value-of-x-if-2-3-x-2-3-x-4-

Question Number 9141 by tawakalitu last updated on 20/Nov/16

Find the value of x if

{(\sqrt{2 + \sqrt{3}})}^{x} + {(\sqrt{2 - \sqrt{3}})}^{x} = 4

Commented by tawakalitu last updated on 20/Nov/16

please help .

Commented by RasheedSoomro last updated on 21/Nov/16

x = 2

Commented by tawakalitu last updated on 21/Nov/16

please working

Commented by sou1618 last updated on 21/Nov/16

\sqrt{2 + \sqrt{3}} = \frac{1}{\sqrt{2 - \sqrt{3}}}

s o

\Leftrightarrow {(\sqrt{2 + \sqrt{3}})}^{x} + {(\sqrt{2 - \sqrt{3}})}^{- x} = 4

t = {(\sqrt{2 + \sqrt{3}})}^{x}

\Rightarrow t + \frac{1}{t} = 4

t^{2} - 4 t + 1 = 0

t = 2 \pm \sqrt{3} = 2 + \sqrt{3}, \frac{1}{2 + \sqrt{3}}

x = 2, - 2

Commented by tawakalitu last updated on 21/Nov/16

Thanks so much sir . God bless you .