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юраісашабрати
@юраісашабрати
August 2022
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[tex]2+ \sqrt{2x-1} =x[/tex]
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nKrynka
2 + √(2x - 1) = x
√(2x - 1) = x - 2
(√(2x - 1))² = (x - 2)²
x - 2 ≥ 0, x ≥ 2, x ∈ [2; + ∞)
2x - 1 = x² - 4x + 4
2x - 1 - x² + 4x - 4 = 0
x² - 6x + 5 = 0
x₁ = 1 не удовлетворяет условию x ∈ [2; + ∞)
x₂ = 5
Ответ: х = 5
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Answers & Comments
√(2x - 1) = x - 2
(√(2x - 1))² = (x - 2)²
x - 2 ≥ 0, x ≥ 2, x ∈ [2; + ∞)
2x - 1 = x² - 4x + 4
2x - 1 - x² + 4x - 4 = 0
x² - 6x + 5 = 0
x₁ = 1 не удовлетворяет условию x ∈ [2; + ∞)
x₂ = 5
Ответ: х = 5