Question

已知,x+y=3,x^3+y^3=1,求xy的值

已知,x+y=3,x^3+y^3=1,求xy的值

Answer 1

由于x+y=3，所以（x+y）^3=27,将左边化开有：x^3+3yx^2+3xy^2+y^3=27,
x^3+y^3+3xy(x+y)=27,1+3xy*3=27，所以xy=26/9

Answer 2

(x+y)^3=27=x^3+y^3+3(x^2)y+3x(y)^2,x^3+y^3=1,3xy(x+y)=9xy,xy=26/9

Answer 3

x^3+y^3=(x+y)*(x^2-xy+y^2)
=>1=3*(x^2-xy+y^2)
=>x^2-xy+y^2=1/3
xy =（x^2-xy+y^2）-（x+y）^2
=1/3-3*2

=-17/3

赏金拿来~~

Answer 4

x^3+y^3=(x+y)*(x^2-xy+y^2)

x^2-xy+y^2=1/3

(x+y)^2-3xy=1/3

3xy=9-1/3=26/3

xy=26/9=2.8888……

Answer 5

x³+y³=1
(x+y)(x²-xy+y²)=1
(x+y)[(x²+2xy+y²)-3xy]=1
(x+y)[(x+y)²-3xy]=1
3(3²-3xy)=1
3(9-3xy)=1
27-9xy=1
9xy=27-1
9xy=26
xy=26/9