已知x+y=m(m不等于0),x的三次方+y的三次方=n,求x的平方+y的平方的值(用含m,n的代

2024-11-18 04:35:25
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回答1:

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)