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Fasolka2001
@Fasolka2001
August 2022
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Решить систему уравнений
x+y=3
x^3+y^3=9
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m11m
Verified answer
X+y=3
x=3-y
x³ + y³ =9
(x+y)(x² -xy+y²)=9
3(x²-xy+y²)=9
x² - xy +y² =3
(3-y)² - (3-y)y +y² =3
9-6y+y² -3y +y² +y² -3=0
3y² -9y +6=0
y² -3y +2=0
y² -2y -y+2=0
(y² -2y)-(y-2)=0
y(y-2)-(y-2)=0
(y-2)(y-1)=0
a) y-2=0
y=2 x=3-2=1
b) y-1=0
y=1 x=3-1=2
Ответ: (1; 2);
(2; 1).
1 votes
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Answers & Comments
Verified answer
X+y=3x=3-y
x³ + y³ =9
(x+y)(x² -xy+y²)=9
3(x²-xy+y²)=9
x² - xy +y² =3
(3-y)² - (3-y)y +y² =3
9-6y+y² -3y +y² +y² -3=0
3y² -9y +6=0
y² -3y +2=0
y² -2y -y+2=0
(y² -2y)-(y-2)=0
y(y-2)-(y-2)=0
(y-2)(y-1)=0
a) y-2=0
y=2 x=3-2=1
b) y-1=0
y=1 x=3-1=2
Ответ: (1; 2);
(2; 1).