1.(lg2)^3+(lg5)^3+3lg2*lg5=2.若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则x/y=

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1.(lg2)^3+(lg5)^3+3lg2*lg5=2.若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则x/y=

1.(lg2)^3+(lg5)^3+3lg2*lg5=2.若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则x/y=
1.(lg2)^3+(lg5)^3+3lg2*lg5=
2.若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则x/y=

1.(lg2)^3+(lg5)^3+3lg2*lg5=2.若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则x/y=
1.设x=lg2,y=lg5,则x+y=lg2+lg5=lg10=1
原式=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
2.
lg(x-y)+lg(x+2y)=lg2+lgx+lgy
lg(x-y)(x+2y)=lg2xy
(x-y)(x+2y)=2xy
x^2+xy-2y^2=2xy
x^2-xy-2y^2=0
设x/y=k
k^2y^2-ky^2-2y^2=0
(k^2-k-2)Y^2=0
k^2-k-2=0
(k+1)(k-2)=0
k=-1,k=2
x/y=-1(舍),x/y=2