Question

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的代数式表示)

Answer 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)