Решение
1.
x⁴ - 5x² - 36 = 0
x² = t, t > 0
t² - 5t - 36 = 0
t₁ = - 4 не удовлетворяет условию t > 0
t² = 9
x² = 9
x₁ = - 3
x₂ = 3
2.
(x² + 3x)² - 2(x² + 3x) - 8 = 0
x² + 3x = t
t² - 2t - 8 = 0
t₁ = - 2
t₂ = 4
1) x² + 3x = - 2
x² + 3x + 2 = 0
x₁ = - 1
x₂ = - 2
2) x² + 3x = 4
x² + 3x - 4 = 0
x₃ = - 4
x₄ = 1
3.
x/(x + 8) + (x + 8)/(x - 8) = (x² + x + 12)*(x² - 64)
(x² - 8x + x² + 16x + 64 - x² - x - 12)/(x² - 64) = 0
x² - 9x - 52 = 0
x² - 64 ≠ 0, x ≠ - 8, x ≠ 8
x² - 9x - 52 = 0
D = 81 + 4*1*52 = 289
x₁ = (9 - 17)/2
x₁ = - 4
x₂ = (9 + 17)/2
x₂ = 13
4.
(2x + 3)*(4x - 3)*0x - 10) ≥ 0
2x + 3 = 0, x = - 1,5
4x - 3 = 0
x = 0,75
x - 10 = 0, x = 10
- + - +
------------------------------------------------------------->
- 1,5 0,75 10 x
x∈[- 1,5; 0,75] [10; + ∞)
5.
- 4x² + 13x - 3 ≥ 0
4x² - 13x + 3 ≤ 0
D = 169 - 4*4*3 = 121
x₁ = (13 - 11)/8
x₁ = 1/4
x₂ = (13 + 11)/8
x₂ = 3 целое
Ответ: х = 3