Решение
√(x + 2) * lg(3x² + 5x - 11) = 0
1) √(x + 1) = 0, x + 1 = 0
x₁ = - 1
2) lg(3x² + 5x - 11) = 0
3x² + 5x - 11 = 10°
3x² + 5x - 11 - 1 = 0
3x² + 5x - 12 = 0
D = 25 + 4*3*12 = 25 + 144 = 169
x₂ = (- 5 - 13)/6
x₂ = - 3
x₃= (- 5 + 13)/6
x₂ = 8/6
x₃ = 4/3
Проверка:
x₂ = - 3
lg [3(- 3)² + 5(- 3) - 11] = lg (27 - 15 - 11) = lg 1 = 0
верно
x₃ = 4/3
lg [3(4/3)² + 5*(4/3) - 11] = lg (16/3 + 20/3 - 11) = lg(36/3 - 11) =
= lg (12 - 11) = lg 1 = 0
верно
Ответ: Уравнение имеет 3 корня.
x₁ = - 1 ; x₂ = - 3 ; x₃ = 4/3 = 1 (1/3)