РЕШИТЕ НЕРАВЕНСТВА: 1.(x-1)(x-6)<50 2.(x-2)(x-14)>64

Предыдущий
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вопрос

Expand the left side of the inequality:
x^2 - 7x + 6 < 50

Subtract 50 from both sides:
x^2 - 7x + 6 - 50 < 0

Combine like terms:
x^2 - 7x - 44 < 0

Now find the roots of the quadratic equation:
x^2 - 7x - 44 = 0
(x - 11)(x + 4) = 0
x = 11 or x = -4

This divides the number line into 3 intervals: (-∞, -4), (-4, 11), (11, ∞)
Choose a test point from each interval to determine the sign of the inequality:
For x = -5: (-5)^2 - 7(-5) - 44 < 0 ----> -25 + 35 - 44 < 0 ----> -34 < 0 (true)
For x = 0: (0)^2 - 7(0) - 44 < 0 ----> -44 < 0 (true)
For x = 12: (12)^2 - 7(12) - 44 < 0 ----> 144 - 84 - 44 < 0 ----> 16 < 0 (false)
Therefore, the solution to the inequality is: -4 < x < 11

Expand the left side of the inequality:
x^2 - 16x + 28 > 64

Subtract 64 from both sides:
x^2 - 16x + 28 - 64 > 0

Combine like terms:
x^2 - 16x - 36 > 0

Now find the roots of the quadratic equation:
x^2 - 16x - 36 = 0
(x - 18)(x + 2) = 0
x = 18 or x = -2

This divides the number line into 3 intervals: (-∞, -2), (-2, 18), (18, ∞)
Choose a test point from each interval to determine the sign of the inequality:
For x = -3: (-3)^2 - 16(-3) - 36 > 0 ----> 9 + 48 - 36 > 0 ----> 21 > 0 (true)
For x = 0: (0)^2 - 16(0) - 36 > 0 ----> -36 > 0 (false)
For x = 19: (19)^2 - 16(19) - 36 > 0 ----> 361 - 304 - 36 > 0 ----> 21 > 0 (true)
Therefore, the solution to the inequality is: x < -2 or x > 18