Question

Извлеките корень
$\sqrt{a {}^{2} - 2 \sqrt{2a + 2} }$

при
а€[-∞;√2]
Ответ должен получиться √2-а​​

Answer 1

$\displaystyle\bf\\\sqrt{a^{2}-2\sqrt{2} a+2 } =\sqrt{a^{2} -2\cdot \sqrt{2} \cdot a+(\sqrt{2})^{2} } =\\\\\\=\sqrt{(a-\sqrt{2} )^{2} } =\Big|a-\sqrt{2} \Big|=\sqrt{2} -a$