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Smeh1312
@Smeh1312
July 2022
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Решите систему уравнений методом замены переменной, пожалуйста
x^3-y^3=28
x^2+xy+y^2=7
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sedinalana
Verified answer
X³-y³=28⇒(x-y)(x²+xy+y²)=28
x²+xy+y²=7
x-y=28:7
x-y=4
x=y+4
(y+4)³-y³=28
y³+12y²+48y+64-y³-28=0
12y²+48y+36=0
y²+4y+3=0
y1+y2=-4 U y1*y2=3
y1=-3⇒x1=-3+4=1
y2=-1⇒x2=-1=4=3
(1;-3);(3;-1)
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Answers & Comments
Verified answer
X³-y³=28⇒(x-y)(x²+xy+y²)=28x²+xy+y²=7
x-y=28:7
x-y=4
x=y+4
(y+4)³-y³=28
y³+12y²+48y+64-y³-28=0
12y²+48y+36=0
y²+4y+3=0
y1+y2=-4 U y1*y2=3
y1=-3⇒x1=-3+4=1
y2=-1⇒x2=-1=4=3
(1;-3);(3;-1)