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已知:x-y=1,求证:x3-3xy-y3=

证明:x3-3xy-y3=x3-y3-3xy=(x-y)(x2+xy+y2)-3xy=x2+xy+y2-3xy=x2-2xy+y2=(x-y)2=1

x^3+y^3+3xy = (x+y)(x^2-xy+y^2)+3xy = x^2-xy+y^2+3xy = x^2+2xy+y^2 = (x+y)^2 = 1 希望你能采纳,不懂可追问。谢谢。

已知x+y=1,求x³+y³+3xy的值 x³+y³+3xy =(x+y)(x²-xy+y²)+3xy =x²-xy+y²+3xy =x²+2xy+y² =(x+y)² =1

x3+3xy+y3=(x+y)(x2-xy+y2)+3xy,=(x2-xy+y2)+3xy,=(x+y)2-3xy+3xy,=1.

求的应该是:x³+3x²y+3xy²+y³ 吧?! . 由已知可得:x+2=0且y+1=0 解得:x=-2,y=-1 所以: x³+3x²y+3xy²+y³ =x³+y³+3x²y+3xy² =(x+y)(x²-xy+y²)+3xy(x+y) =(x+y)(x...

(1)∵x+y=1,xy=-3,∴原式=(x+y)2-2xy=1+6=7;(2)原式=(x+y)(x2-xy+y2)=7+3=10;(3)原式=xy(x4+y4)=xy[(x2+y2)2-2x2y2]=-93.

x^2+y^2+z^2 =(x+y+z)^2-2(xy+xz+yz) =9+2 =11 1/x+1/y+1/z =yz/xyz+xz/xyz+xy/xyz =(yz+xz+xy)/xyz =-1/2

求z=x³+y³-3xy的极值 解:令 ∂z/∂x=3x²-3y=0,得y=x²..........① 再令 ∂z/∂y=3y²-3x=0,得x=y²..............② 将①代入②式得x=x^4,即x^4-x=x(x³-1)=x(x-1)(x²+x+1)=0,得x...

z=x^3+y^3-3xy ∂z/∂x=3x²-3y ∂z/∂y=3y²-3x 驻点:(1,1) (0,0) ∂²z/∂x²=6x ∂²z/∂x∂y=3 ∂²z/∂y²=6y (1,1) A=6 B=3 C=6 B²-AC=9-360 ...

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