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.

wit1192022-10-04 11:39:544条回答

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balance0211 共回答了18个问题 | 采纳率83.3%
=(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
1年前
liedd 共回答了5个问题 | 采纳率
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
1年前
zhangbing8211 共回答了1260个问题 | 采纳率
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
1年前
stray-bird 共回答了11个问题 | 采纳率
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
1年前

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