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LubaIvanova160
@LubaIvanova160
July 2022
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x - 2√x - 6=0
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Dимасuk
Verified answer
Пусть t = √x, t ≥ 0
t² - 2t - 6 = 0
D = 4 + 6·4 = 28 = (2√7)²
t₁ = (2 + 2√7)/2 = 1 + √7
t₂ = (2 - 2√7)/2 = 1 - √7 < 0 ⇒ посторонний корень
Обратная замена:
√x = 1 + √7
x = (1 + √7)²
x = 1 + 7 + 2√7
x = 8 + 2√7
Ответ: x = 8 + 2√7.
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Answers & Comments
Verified answer
Пусть t = √x, t ≥ 0t² - 2t - 6 = 0
D = 4 + 6·4 = 28 = (2√7)²
t₁ = (2 + 2√7)/2 = 1 + √7
t₂ = (2 - 2√7)/2 = 1 - √7 < 0 ⇒ посторонний корень
Обратная замена:
√x = 1 + √7
x = (1 + √7)²
x = 1 + 7 + 2√7
x = 8 + 2√7
Ответ: x = 8 + 2√7.