Question

Матричное неравенство

Answer 1

$1)\; \; \left|\begin{array}{cc}1&x+5\\2&x\end{array}\right|<0\\\\x-2(x+5)<0\; ,\; \; \; x-2x-10<0\; ,\; \; \; -x<10\; ,\; \; \underline {x>-10}$

$2)\; \; \left|\begin{array}{ccc}2&x+2&-1\\1&1&-2\\5&-3&x\end{array}\right|>0\\\\2\, (x-6)-(x+2)(x+10)-(-3-5)>0\\\\2x-6-(x^2+12x+20)+8>0\\\\-x^2-10x-18>0\\\\x^2+10x+18<0\\\\D/4=5^2-18=7\; ,\; \; x_{1,2}=-5\pm \sqrt7\; \; \to \\\\(x+5+\sqrt7))(x+5-\sqrt7)<0\\\\znaki:\; \; \; +++(-5-\sqrt7)---(-5+\sqrt7)+++\\\\x\in (-5-\sqrt7\, ;\, -5+\sqrt7)$