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Lusinbri12
@Lusinbri12
July 2022
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Выпишите формулы Виета для заданного уравнения и укажите его корни:
x^2-3√2 *x+4=0
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Verified answer
Х₁ * х₂ = 4
х₁ + х₂ = 3√2
-----------------система
х₁ = 3√2 - х₂
(3√2 - х₂) * х₂ = 4
х₂² - 3√2*х₂ + 4 = 0
D=18-4*4=2
х₂ = (3√2 - √2)/2 = √2 х₁ = 3√2 - √2 = 2√2
х₂ = (3√2 + √2)/2 = 2√2 х₁ = 3√2 - 2√2 = √2
Ответ: √2 и 2√2
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Answers & Comments
Verified answer
Х₁ * х₂ = 4х₁ + х₂ = 3√2
-----------------система
х₁ = 3√2 - х₂
(3√2 - х₂) * х₂ = 4
х₂² - 3√2*х₂ + 4 = 0
D=18-4*4=2
х₂ = (3√2 - √2)/2 = √2 х₁ = 3√2 - √2 = 2√2
х₂ = (3√2 + √2)/2 = 2√2 х₁ = 3√2 - 2√2 = √2
Ответ: √2 и 2√2