Question

Решите неравенства и уравнения

Answer 1

$x^3-x^2-\frac{8}{x^3-x^2}=2;\\ OD3: x^3-x^2\neq 0, x^2(x-1)\neq 0\Rightarrow x\neq 0;1.\\x^3-x^2=t\neq 0;\\t-\frac{8}{t}-2=0|\cdot t\\\\t^2-2t-8=0\Rightarrow t_1=-2, t_2=4;\\\\1) x^3-x^2=-2;\\\\x^3-x^2+2=0;\\x^3+x^2-2x^2+2=0;\\x^2(x+1)-2(x^2-1)=0;\\x^2(x+1)-2(x-1)(x+1)=0;\\(x+1)(x^2-2x+2)=0\Rightarrow x = -1.$

$2) x^3-x^2=4,\\\\x^3-2x^2+x^2-4=0;\\x^2(x-2)+(x-2)(x+2)=0\\\\(x-2)(x^2+x+2)=0\Rightarrow x = 2.$

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