4. Решите систему неравенство
{х²-х+6>0
{ (х-5)(х+5)\<
!!

Объяснение:

The first inequality can be solved by factoring the quadratic expression and analyzing the sign of the factors:

x² - x + 6 > 0

The discriminant is negative (Δ = (-1)² - 4(1)(6) = -23), indicating that there are no real roots. Therefore, the quadratic expression is always positive, and the inequality holds for all values of x.

x² - x + 6 > 0 is true for all x.

The second inequality can be solved by applying the zero product property:

(х-5)(х+5) ≤ 0

The factors can have opposite signs or be equal to zero for this inequality to hold. Therefore, we can set up the following intervals:

x ≤ -5 or x ≥ 5

The solution to the inequality is the union of these two intervals:

x ≤ -5 or x ≥ 5

{x | x ≤ -5 or x ≥ 5}