Question

Уравнения 1. (x^2+4)^2-7(x^2+4)+10=0 2. 2x^3-x^2+2x-1=0

Answer 1

$1)\; \; (x^2+4)^2-7(x^2+4)+10=0\\\\t=x^2+4\; ;\; \; t^2-7t+10=0\\\\t_1=2\; ;\; t_2=5\\\\x^2+4=2\; \; \to \; \; x^2=-2\ \textless \ 0\; \; net\; reshenij,\; t.k.\; x^2 \geq 0\\\\x^2+4=5\; \; \to \; \; x^2=1\; ,\; x=\pm 1\\\\Otvet:x=-1\; ;\; x=1.\\\\2)\; \; 2x^3-x^2+2x-1=0\\\\x^2(2x-1)+(2x-1)=0\\\\(2x-1)(x^2+1)=0\\\\x^2+1=0\; net\; reshenij,\; t.k.\; x^2+1\ \textgreater \ 0\\\\2x-1=0\; ;\; x=\frac{1}{2}\\\\Otvet:\; x=\frac{1}{2}$