x-x-x-1-2-x-

Question Number 120545 by pooooop last updated on 01/Nov/20

{(\sqrt{x})}^{\frac{x}{\sqrt{x}}} = \frac{1}{\sqrt{2}} x = ?

Commented by pooooop last updated on 01/Nov/20

{(\sqrt{x})}^{\frac{x \sqrt{x}}{x}} = {(\frac{1}{2})}^{\frac{1}{2}}

Commented by pooooop last updated on 01/Nov/20

\sqrt{x} = \frac{1}{2} => x = \frac{1}{4}

Answered by Jamshidbek2311 last updated on 01/Nov/20

\sqrt{x} = a ⩾ 0

a^{\frac{a^{2}}{a}} = \frac{1}{\sqrt{2}} \Rightarrow a^{a} = {(\frac{1}{2})}^{\frac{1}{2}} \Rightarrow a = \frac{1}{2}

\sqrt{x} = \frac{1}{2} \Rightarrow x = \frac{1}{4}