x^2+y^2+xy=1

符翰苛1591[x^2y^2(x+y)^2 - xy^2(x^3+xy^2)]/(1/2x^2y),其中x=1/2,y=1 -
潘空很15067571642 ______ [x^zhidao2y^2(x+y)^2-xy^2(x^3+xy^2)]/(1/2x^2y)=[x^2y^2(x+y)^2-x^2y^2(x^2+y^2)]/(1/2x^2y)={x^2y^2[(x+y)^2-x^2-y^2]}/(1/2x^2y)=x^2y^2[x^2+2xy+y^2-x^2-y^2]/(1/2x^2y)=x^2y^2(2xy)/(1/2x^2y)=x^2y^2(2xy)*[2/(x^2y)]=4xy^2=4*(1/2)*1=2

符翰苛1591已知x+y=4,xy=3,求:(1)x^2y - xy^2;(2)(x^2+1)(y^2+1)求解 -
潘空很15067571642 ______ (x-y)^2=(x+y)^2-4xy=16-12=4 x-y=+-21)x^2y-xy^2=xy(x-y)=+-6 (2)(x^2+1)(y^2+1)=x^2t^2+x^2+y^2+1=x^2y^2+(x+y)^2-2xy+1=9+16-6+1=20

符翰苛1591已知x^2+y^2 - 2x - 6y+10=0求(x - y)(x^2+3xy - y^2) - 5xy(x - y)的值
潘空很15067571642 ______ 解:因为x^2+y^2-2x-6y+10=0, 所以(x^2-2x+1)+(y^2-6y+9)=0, 则(x-1)^2+(y-3)^2=0, 则x=1,y=3. (x-y)(x^2+3xy-y^2)-5xy(x-y) =(x-y)(x^2-y^2-2xy) =(x-y)[(x+y)(x-y)-2xy] =(x+y)(x-y)^2-2xy(x-y) =(1+3)*(1-3)^2-2*1*3*(1-3) =16+12 =28.

符翰苛1591已知x - y=2,xy=80,求(1)x^2+Y^2的值;(2)(x+y)^2的值 -
潘空很15067571642 ______ 因为(X-Y)^2=X^2-2XY+Y^2=4 所以 X^2+Y^2=2XY+4 引文XY=80 2XY=160 所以 X^2+Y^2=2XY+4=160+4=164 (X+Y)^2=X^2+2XY+Y^2=X^2-2XY+Y^2+4XY=(X-Y)^2+4XY=4+320=324 希望对你有帮助.

符翰苛1591x^2+y^2=25 xy=12 x - y等于多少
潘空很15067571642 ______ x^2+y^2-2xy+2xy=25 得(x-y)^2+2xy=25 (x-y)^2=25-2*12=1 所以(x-y)=1或-1

符翰苛1591x^2+y^2=25,x+y=7,x>y,则x - y的值等于 -
潘空很15067571642 ______ (x+y)2=49 2xy=24 (x-y)2=x2+y2-2xy=1 x-y=1

符翰苛1591已知x - y=1,x^3 - y^3=2,求x^4+y^4的值
潘空很15067571642 ______ x^3-y^3=2 (x-y)(x^2+xy+y^2)=2 x-y=1 (x^2+xy+y^2)=2 (x-y)^2+3xy=2 1+3xy=2 xy=1/3 (x^2+xy+y^2)=2 x^2+y^2=2-xy x^2+y^2=2-1/3=5/3 x^4+y^4=(x^2+y^2)^2-2x^2y^2=(5/3)^2-2(xy)^2=25/9-2(1/3)^2=25/9-2/9=23/9

符翰苛1591分解因式 (x^2+2)(x^2 - 1) - 18 (xy+1)(x+1)(y+1)+xy (x+1)(x+2)(x+4)(x+5)+2
潘空很15067571642 ______ (x^2+2)(x^2-1)-18=x^4+x^2-2-18=x^4+x^2-20=(x^2+5)(x^2-4) (xy+1)(x+1)(y+1)+xy=(xy+1)(xy+1+x+y)+xy=(xy+1)(xy+x+1)+y(xy+1)+xy =(xy+1)(xy+x+1)+y(xy+1+x)=(xy+x+1)(xy+y+1) (x+1)(x+2)(x+4)(x+5)+2=(x+1)(x+5)(x+2)(x+4)+2 =(x^2+6x+5)(x^2+6x+8)+2 =(x^2+6x)^2+13(x^2+6x)+40+2=(x^2+6x)^2+13(x^2+6x)+42 =(X^2+6x+6)(x^2+6x+7)

符翰苛1591若x+y=4,xy=3,则x^2+y^2= 若x^2 - 2x+y^2 +6x+10=0,则x - y= 若m^2 +m - 1=0,则m^3 +2m^2 +2011= -
潘空很15067571642 ______ x^2+y^2=(x+y)^2-2xy=16-6=10 x^2 -2x+y^2 +6y+10=0(x-1)^2+(y+3)^2=0 x-1=0 y+3=0 x=1 y=-3 x-y=1+3=4 m^2 +m-1=0,m^2 +m=1 m^3 +2m^2 +2011=m(m^2+m+m)+2011=m(1+m)+2011=m^2+m+2011=1+2011=2012