Question

верно ли равенство x√6 =√6x2​

Answer 1

Ответ:

$\sqrt{6x^2}=|x|\sqrt6=\left\{\begin{array}{l}x\sqrt6\ ,\ esli\ x\geq 0\ ,\\-x\sqrt6\ ,\ esli\ x<0\ .\end{array}\right\\\\\\x=4\geq 0\ \ \ \to \ \ x\sqrt6=\sqrt{6x^2}\ \ ,\ \ 4\sqrt6=\sqrt{6\cdot 4^2}=\sqrt{96}\\\\x=-5<0\ \ \to \ \ x\sqrt6=-\sqrt{6x^2}=-\sqrt{6\cdot 5^2}=-\sqrt{150}\\\\x\geq 0\ \ \ \to \ \ \ x\sqrt6=\sqrt{6x^2}\\\\x\leq 0\ \ \ \to \ \ \ x\sqrt6=-\sqrt{6x^2}$

Заданное равенство верно при   $x=-5$  и  при   $x\leq 0\ .$