Question

1)$sqrt{2x+1} = sqrt{ x^{2} -2x+4}$
2)$sqrt{x} = sqrt{ x^{2} -x-3}$
3)$sqrt{x+2} = sqrt{2x-3}$
4)$sqrt{9- x^{2} } = sqrt{x+9}$

Answer 1

1) ОДЗ: х ≥ -0,5
2x + 1 = x² - 2x + 4
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0
x₁ = 1; x₂ = 3

2) х ≥ 0
x = x² - x - 3
x² - 2x - 3 = 0
(x - 3)(x+1) = 0
x₁ = -1 - не подходит
x₂ = 3
Ответ: 3

3) x ≥ - 2
x + 2 = 2x - 3
x = 5

4) ОДЗ: [-3; 3]
9 - x² = x + 9
x² + x = 0
x₁ = 0
x₂ = -1