(lg2)^3+(lg5)^3+3lg2*lg5的值为?

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(lg2)^3+(lg5)^3+3lg2*lg5的值为?
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(lg2)^3+(lg5)^3+3lg2*lg5的值为?
(lg2)^3+(lg5)^3+3lg2*lg5的值为?

(lg2)^3+(lg5)^3+3lg2*lg5的值为?
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
解毕!