Question

помогите пожалуйста, даю 40 баллов
x^2+(18/x)=6+6x-(9/(x^2))

Answer 1

$x^2+\frac{18}{x}=6+6x-\frac{9}{x^2}\\x^2+\frac{18}{x}=6+6x-\frac{9}{x^2},x\neq0\\x^2+\frac{18}{x}-6-6x+\frac{9}{x^2}=0\\\frac{x^4+18-6x^2-6x^3+9}{x^2}=0\\x^4+18x-6x^2-6x^3+9=0\\x^4+18x-3x^2-3x^2-6x^3+9=0\\x^2\cdot(x^2-3)-6x\cdot(x^2-3)-3(x^2-3)=0\\(x^2-3)\cdot(x^2-6x-3)=0\\x^2-3=0\\\\x^2-6x-3=0\\x=-\sqrt{3}............x\neq0\\x=3+2\sqrt{3}\\x=3-2\sqrt{3}\\\\x=-\sqrt{3}\\x=\sqrt{3}\\x=3+2\sqrt{3}\\x=3-2\sqrt{3}\\x_1=-\sqrt{3},x_2=3-2\sqrt{3},x_3=\sqrt{3},x_4=3+2\sqrt{3}$