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Danil02280
@Danil02280
July 2022
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дано уравнение х^2+x-5=0.найдите сумму квадратов его корней.
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nKrynka
Решение
x² + x - 5 = 0
D = 1 + 4*1*5 = 21
x₁ = (- 1 - √21)/2
x₂ = (-1 + √21)/2
x₁² + x² = [ (- 1 - √21)/2]² + (- 1 + √21)/2]² =
(1 - 2√21 + 21 + 1 + 2√21 + 21)/4 = 44/4 = 11
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Answers & Comments
x² + x - 5 = 0
D = 1 + 4*1*5 = 21
x₁ = (- 1 - √21)/2
x₂ = (-1 + √21)/2
x₁² + x² = [ (- 1 - √21)/2]² + (- 1 + √21)/2]² =
(1 - 2√21 + 21 + 1 + 2√21 + 21)/4 = 44/4 = 11