解(1g2)^3+(1g5)^3+1g5*1g8

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解(1g2)^3+(1g5)^3+1g5*1g8

解(1g2)^3+(1g5)^3+1g5*1g8
解(1g2)^3+(1g5)^3+1g5*1g8

解(1g2)^3+(1g5)^3+1g5*1g8
令x=lg2,y=lg5,x+y=lg2+lg5=lg10=1
x³+y³+y*(3x)
=(x+y)³-3xy(x+y)+3xy
=1³-3xy+3xy
=1

=(lg2)^3+(lg5)^3+3lg5*lg2=(lg2)^3+(lg5)^3+3lg5*lg2*1=(lg2)^3+(lg5)^3+3lg5*lg2*(lg2+lg5)=(lg2)^3+(lg5)^3+3(lg2)^2*(lg5)+3(lg5)^2=(lg2+lg5)^3=1