Решите уравнение, используя введение новой переменной [latex](x^2-4)|x|+3=0[/latex]

[latex](x^2-4)\cdot |x|+3=0\\\\Formyla:\quad x^2=|x|^2\\\\(|x|^2-4)\cdot |x|+3=0\\\\t=|x|\; \; \to \; \; (t^2-4)\cdot t+3=0\; ,\quad t \geq 0\\\\t^3-4t+3=0\\\\Pri\; \; t=1:\; \; 1^3-4\cdot 1+3=0\; \; \to \; \; t^3-4t+3=(t-1)\cdot (t^2+t-3)\\\\t^2+t-3=0\; \; \to \; \; D=1+12=13\\\\t_1= \frac{-1-\sqrt{13}}{2} \ \textless \ 0\;\; \; t_2= \frac{-1+\sqrt{13}}2} \approx 1,3\ \textgreater \ 0[/latex] [latex]a)\; \; |x|=1\quad \to \quad x=\pm 1\\\\b)\quad |x|=\frac{\sqrt{13}-1}{2}\quad \to \quad x=\pm \frac{\sqrt{13}-1}{2}\\\\Otvet:\quad -1;\; 1;\; -\frac{\sqrt{13}-1}{2};\; \frac{\sqrt{13}-1}{2}\; .[/latex]