Неравенства по алгебре 1) (sqrt(13-7x-6x^2))/12>=1
2)(x-3)*sqrt(x^2+3)<=x^2-9

Предыдущий
вопрос Следующий
вопрос

1) (sqrt(13-7x-6x^2))/12 >= 1
Square both sides to eliminate the square root:
13 - 7x - 6x^2 >= 144
Rearrange the inequality:
6x^2 + 7x - 131 <= 0
Factor the quadratic equation:
(3x - 17)(2x + 19) <= 0
The critical points are x = 17/3 and x = -19/2. Test the intervals (-∞, -19/2), (-19/2, 17/3), and (17/3, ∞) to determine where the inequality holds true. The final solution will be the interval where the inequality is true.

2) (x-3)sqrt(x^2+3) <= x^2 - 9
Square both sides to eliminate the square root:
(x-3)^2 (x^2 + 3) <= (x^2 - 9)^2
Expand both sides:
x^5 - 9x^4 - 3x^3 + 27x^2 - 9x^2 + 81 <= x^4 - 18x^2 + 81
Combine like terms:
x^5 - 9x^4 - 3x^3 + 36x^2 - x^4 + 18x^2 - 81 <= 0
Simplify further:
x^5 - 10x^4 - 3x^3 + 54x^2 - 81 <= 0
This is a fifth-degree polynomial inequality. Its solution involves determining the roots of the polynomial and finding the intervals where the inequality holds true.