Решите систему неравенств: {(x2+1)(x2+3)(x2−2)≥0 {x<3

Question

Решите систему неравенств:
{(x2+1)(x2+3)(x2−2)≥0
{x<3

Answer 1

{x<3<br>{(x²+1)(x²+3)(x²-2)≥0
x²+1>0 U x²+3>0 при любом х⇒x²-2≥0
(x-√2)(x+√2)≥0
x=√2  x=-√2
 //////////////////                                \\\\\\\\\\\\\\\\\\\\\\\\
             +                    _                        +
---------------[-√2]-----------------[√2]---------(3)---------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(-∞;-√2] U [√2;3)