x2 - 20x > -11x-7 -x2

Предыдущий
вопрос Следующий
вопрос

To solve this inequality, we first need to simplify the expression:

x2 - 20x > -11x - 7 - x2
2x2 - 20x + 11x + 7 > 0
2x2 - 9x + 7 > 0

Next, we will find the critical points by setting the inequality to equal zero:

2x2 - 9x + 7 = 0
(x - 1)(2x - 7) = 0

x = 1 or x = 7/2

Now we can test each interval created by the critical points to determine when the inequality is true:

Interval 1: (-∞, 1)
Pick x = 0: 2(0)2 - 9(0) + 7 = 7 > 0

Interval 2: (1, 7/2)
Pick x = 2: 2(2)2 - 9(2) + 7 = 8 - 18 + 7 = -3 < 0

Interval 3: (7/2, ∞)
Pick x = 4: 2(4)2 - 9(4) + 7 = 32 - 36 + 7 = 3 > 0

Therefore, the solution to the inequality is x < 1 or x > 7/2.