Question

مطلوب است محاسبه xدر صورتی که: $ \frac{x}{ \sqrt{2} }=\sqrt({2}( ^{ \frac{x}{ \sqrt{2} } } )^{ \frac{1}{ \sqrt{2} } }) $

Answer 1

$$( \frac{x}{ \sqrt{2} } )^{ \frac{1}{ \sqrt{2} } } =a \Longrightarrow \frac{x}{ \sqrt{2} } = a^{ \sqrt{2} } \Longrightarrow a^{ \sqrt{2} } = \sqrt{ 2^{a} } \Longrightarrow a^{2 \sqrt{2} } = 2^{a} \Longrightarrow a^{2}=2;;a= \sqrt{2} \Longrightarrow a= \sqrt{2} \Longrightarrow ( \frac{x}{ \sqrt{2} } )^{ \frac{1}{ \sqrt{2} } }= \sqrt{2} \Longrightarrow \frac{x}{ \sqrt{2} } = \sqrt{2} ^{ \sqrt{2} } \Longrightarrow x= ( \sqrt{2} )^{ \sqrt{2} +1} $$