Question

Rezolvat sistemul:
2(x^3+y^3)=9xy
x+y=3

Answer 1

2x^3+2y^3

x=3-y

2(3-y)^3+2y^3=9(3-y)y

2(27-27y+9y^2-y^3)+2y^3=9(3-y)y

2(27-27y+9y^2-y^3)+2y^3=27y-9y^2

54-54y+18y^2-2y^3=27y-9y^2

54-54y+18y^2=27y-9y^2

54-81y+27y^2=0

27y^2-81y+54=0

27(y^2-3y+2)=0/:27

y^2-3y+2=0

y^2-y-2y+2=0

y(y-1)-2(y-1)=0

(y-1)(y-2)=0

PRIMUL CAZ

y-1=0=>y=1

x=3-1=2

AL DOILEA CAZ

y-2=0=>y=2

x=3-2=1

(x;y)=(1;2)

(x;y)=(1;2)(x;y)=(2;1)