√(2x + 3) + √(x - 2) = 4
ОДЗ:
2x + 3 ≥ 0
x - 2 ≥ 0
x ≥ 2
√(2x + 3) = 4 - √(x - 2)
2x + 3 = 16 - 8√(x - 2) + x - 2
2x - x + 3 - 16 + 2= -8√(x - 2)
x - 11 = -8√(x - 2)
11 - x = 8√(x - 2) 11 - x ≥ 0
121 - 22x + x² = 64x - 128 x ≤ 11
x² - 86x + 249 = 0
x₁ + x₂ = 86
x₁x₂ = 249
x₁ = 3; x₂ = 83 - не уд. условию x ≤ 11
Ответ: x = 3.