已知X-Y=1 XY=2 X2Y-2X2Y2+XY3
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x2y+xy2-x-y=xy(x+y)-(x+y)=(x+y)(xy-1)∵x+y=-5,xy=7,∴原式=-5×(7-1)=-30.
(x+y)(xy)=x^2y+xy^2=-8原式=-7
x+y+xy=9x+y=9-xyx^2y+xy^2=20xy(x+y)=20xy(9-xy)=20xy^2-9xy+20=0(xy-4)(xy-5)=0xy=4或xy=5x+y=5或x+y=4x^2+
由已知:xy+x+y=17,xy(x+y)=66,可知xy和x+y是方程t2-17t+66=0的两个实数根,得:t1=6,t2=11.即xy=6,x+y=11,或xy=11,x+y=6.x2+y2=(
①x2y+xy2=xy(x+y)=1×3=3;②x2+y2=(x+y)2-2xy=32-2×1=7.
[2x(x2y-xy2)+xy(xy-x2)]÷x2y=[2x3y-2x2y2+x2y2-x3y]÷x2y=x-y,把x=2013,y=2012代入上式得:原式=x-y=2013-2012=1.
原式=2x2y+2xy-3x2y-3xy-4x2y=-5x2y-xy当x=-2,y=12时,原式=-9.
∵x+y=6,xy=4,∴x2y+xy2=xy(x+y)=4×6=24.故答案为:24.
x3+y3-x2y-xy2=(x+y)(x2-xy+y2)-xy(x+y)=(x+y)(x2-2xy+y2)=(x+y)(x2+2xy+y2-4xy)=(x+y)[(x+y)2-4xy]=10×(10
原式=4x2y-6xy+3(4xy-2)+x2y+1=5x2y+6xy-5当x=2,y=-12时,原式=5×4×(-12)+6×2×(-12)-5=-21.
那个2是平方吧?可以用^代替原式=x^y+xy^=xy(x+y)=-3*6=-18
解-x²y-xy²=-xy(x+y)=-2×5=-10
原式=y(x2+2x+1)=y(x+1)2,故答案为:y(x+1)2.
若是209,则xy=8,x+y=15,算出x,y就不是整数了,与题意不符.若是34,x,y为3,5,符合题意.
(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)/(2y)=X^2-y^2-y^2+X^2+y^2-2xy-3x^2+xy=-x^2-y^2-xy=-(x^2+y^2+xy-3
由题意得(x-2)平方+(y-2)平方+(x-y)平方=0,故x=y=2,故x平方y=8
原式=2x2y+2xy-3x2y+3xy-4x2y=-5x2y+5xy,当x=-1,y=1时,原式=-5×(-1)2×1+5×(-1)×1=-5-5=-10.
原式=-xy(x-y),当x-y=3,xy=-2时,则原式=-3×(-2)=6.故答案为:6.
xy+x+y=23,x²y+xy²=120,xy(x+y)=120把xy,x+y看成是z²-23z+120=0的两根解得z1=15,z2=8又把x,y看成是m²
∵x+2y=5,xy=1,∴2x2y+4xy2=2xy(x+2y)=2×1×5=10,故答案为:10.