Question

Решите уравнение: х2 - 6|х| - 16 = 0
помогите пожалуйста,заранее спасибо<3​

Answer 1

$\displaystyle\bf\\x^{2} -6|x|-16=0\\\\ |x|=m \ \ ; \ \ m\geq 0\\\\|x|^{2} -6|x|-16=0\\\\m^{2} -6m-16=0\\\\D=(-6)^{2} -4\cdot(-16)=36+64=100=10^{2} \\\\m_{1}=\frac{6+10}{2} =8\\\\\\m_{2} =\frac{6-10}{2} =-2<0-neyd\\\\|x|=8\\\\\left[\begin{array}{ccc}x_{1} =-8\\x_{2} =8\end{array}\right\\\\\\Otvet:-8 \ ; \ 8$