Question

Решите систему неравенств (x^2+1)(x^2+3)(x^2-2) больше или равно 0

Answer 1

(x^2+1)(x^2+3)(x^2-2)>=0
(x^4+3x^2+x^2+3)*(x^2-2)>=0
x^6-2x^4+3x^4-3x^2+x^4-2x^2+3x^2-6>=0
x^6+2x^4-2x^2-6>=0
t=x^2
t^3+2t^2-2t-6>=0
t(t^2+2t-2)-6>=0
t1>=6

t^2+2t-2=0
D=4+4=8=3^3
t2=(-2-3)/2=-2.5  ||  t3=(-2+3)/2=0.5

x1=6^2=36
x2=(-2.5)^2=6.25
x3=(0.5)^2=0.25