Question

已知x+y=m,x^3+y^3=n,m不等于0,x^2+y^2=?

Answer 1

已知x+y=m
（x+y)²=m²
x²+y²=m²-2xy
x^3+y^3=（x+y）（x²-xy+y²）=n
即m（m²-3xy）=n
xy= (m^3-n)/3m
x²+y²=m²-2xy
=m²-【2(m^3-n)/3m】
=【m^3+2n】/ 3m

Answer 2

(x+y)³=x³+3x²y+3xy²+y³=n+3xy(x+y)=n+3xym=m³
所以xy=(m³-n)/(3m)
所以x²+y²=(x+y)²-2xy=m²-[2(m³-n)/(3m)]=(m³+2n)/(3m)

Answer 3

因为（x+y）^3=x^3+3x^2y+3xy^2+y^3=x^3+y^3+3xy(x+y)=n+3xym=m^3
所以xy=m^3-n/(3m)
x^2+y^2=(x+y)^2-2xy=m^2-2/3(m^2-n/m)=m^2/3+2/3(n/m)
故x^2+y^2=m^2/3+2/3(n/m)

Answer 4

(m^3+2n)/3m