Question

当x+y=5,xy=-3时，求代数式x^3+y^3+x^2y+xy^2的值。今日完成。。。。

当x+y=5,xy=-3时，求代数式x^3+y^3+x^2y+xy^2的值。

Answer 1

=(x³＋y³)＋xy(x＋y)
=(x＋y)(x²－xy＋y²)＋xy(x＋y)
=(x＋y)(x²＋y²)
=(x＋y)[(x＋y)²－2xy]
=5[25＋6]
=155

Answer 2

x+y=5,xy=-3
x^3+y^3+x^2y+xy^2
=(x+y)(x²-xy+y²)+xy(x+y)
=(x+y)(x²+y²)
=(x+y)(x+y)²-2xy
=(x+y)³-2xy
=5³+6
=131

Answer 3

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

=(x^2+y^2)(x+y)
=(x^2++2xy+y^2-2xy)(x+y)
=[(x+y)^2-2xy](x+y)

代入=(25+6)*5=155

Answer 4

原代数式可化为：
=（x^3+x^2y）+（y^3+xy^2）=x^2(x+y)+y^2(x+y)=5x^2+5y^2=5(x^2+y^2)
=5[(x+y)^2-2xy]=5[5^2-2*(-3)]=155