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Темур2106
@Темур2106
July 2022
1
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25 баллов! Сколько различных решений имеет уравнение?
(х^2+4ху+4у^2)^2 + (х^2-2у-1)^2 = 0
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oganesbagoyan
Verified answer
(x² +4xy+4y²) +(x² -2y -1)² =0 ;
(x+2y)² +(x² -2y-1)² =0 ⇔{ x+2y =0 ; x² -2y-1 =0 || суммируем.
x² +x -1 =0 ;
x₁ = (-1-√5)/2 ⇒y₁ = -x₁/2 =(1+√5)/4. * * *x+2y =0⇒у = - x/2 * * *
x₂ = (-1+√5)/2⇒y₂ = -x₂/2 =(1-√5)/4.
ответ : {
(
-(1+√5)/2 ; (1+√5)/4
)
,
(
(√5 -1)/2 ; (1-√5)/4
)
}. =ДВА=
2 votes
Thanks 1
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Verified answer
(x² +4xy+4y²) +(x² -2y -1)² =0 ;(x+2y)² +(x² -2y-1)² =0 ⇔{ x+2y =0 ; x² -2y-1 =0 || суммируем.
x² +x -1 =0 ;
x₁ = (-1-√5)/2 ⇒y₁ = -x₁/2 =(1+√5)/4. * * *x+2y =0⇒у = - x/2 * * *
x₂ = (-1+√5)/2⇒y₂ = -x₂/2 =(1-√5)/4.
ответ : { ( -(1+√5)/2 ; (1+√5)/4 ) , ( (√5 -1)/2 ; (1-√5)/4 ) }. =ДВА=