Question

Помогите с ходом решенияx^3+6x^2+((28x^2+2x-10)/(x-5))<=2

Answer 1

x^3+6x^2+((28x^2+2x-10)/(x-5))<=2
(x^4+6x³-5x³-30x²+28x²+2x-10)/(x-5)-2≤0
(x^4+x³-2x²+2x-10-2x+10)/(x-5)≤0
(x^4+x³-2x²)/(x-5)≤0
x²(x²+x-2)/(x-5)≤0
x²+x-2=0⇒x1+x2=-1 U x1*x2=-2⇒x1=-2 U x2=1
x²(x+2)(x-1)/(x-5)≤0
x=0  x=-2  x=1  x=5
          _               +                   +                   _                    +
-------------[-2]--------------[0]--------------[1]---------------(5)--------------
x∈(-∞;-2] U [1;5) U {0}