Question

Найдите значение выражения $\frac{ \sqrt{ x^{2}-2 \sqrt{2}x+2 }+ \sqrt{ x^{2} +2 \sqrt{2}x + 2 } }{ \sqrt{2} }$

Answer 1

 $\frac{\sqrt{x^2-2\sqrt{2}x+2}+\sqrt{x^2+2\sqrt{2}x+2} } {\sqrt{2} } = \frac{ \sqrt{(x-\sqrt{2})^2}+\sqrt{(x+\sqrt{2})^2}}{ \sqrt{2} }\\ x \leq \sqrt{2}\\ \frac{ \sqrt{2}-x+x+\sqrt{2}}{ \sqrt{2}} = 2\\\\ x \geq \sqrt{2}\\ \frac{ x-\sqrt{2} + x+\sqrt{2}}{ \sqrt{2}} = \sqrt{2}x$