已知x+y=m,x³+y³=n,求x²+y²

已知x+y=m,x³+y³=n,求x²+y²
已知x+y=m,x³+y³=n,求x²+y²

已知x+y=m,x³+y³=n,求x²+y²
x³+y³=n
(x+y)(x²-xy+y²)=n
(x+y)[(x+y)²-3xy]=n
x+y=m代入
m(m²-3xy)=n
m²-3xy=n/m
xy=(m³- n)/(3m)
x²+y²=(x+y)²-2xy=m²-2(m³-n)/(3m)=(3m³-2m³+2n)/(3m)=(m³+2n)/(3m)=m²/3 +2n/(3m)