решите методом подстановки систему x^2-3y^2=12 x+y=6. Created by lindoalena. algebra-ru

решите методом подстановки систему x^2-3y^2=12 x+y=6...

lindoalena @lindoalena

July 2022 1 6 Report

решите методом подстановки систему

x^2-3y^2=12
x+y=6

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ShirokovP

Verified answer

X^2 - 3y^2 = 12
x + y = 6

x^2 - 3y^2 = 12
y = 6 - x

x^2 - 3 (6 - x)^2 - 12 = 0
x^2 - 3 (x^2 - 12x + 36) - 12 = 0
x^2 - 3x^2 + 36x - 108 - 12 = 0
- 2x^2 + 36x - 120 = 0 // : (-2)
x^2 - 18x + 60 = 0
D = 324 - 240 = 84
x₁ = ( 18 + 2√21)/2 = 9 + √21
x₂ = ( 18 - 2√21)/2 = 9 - √21

x₁ = 9 + √21
y₁ = 6 - (9 + √21) = - 3 - √21

x₂ = 9 - √21
y₂ = 6 - (9 - √21) = - 3 + √21

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lindoalena August 2022 | 0 Ответы

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