2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=?

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2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=?

2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=?
2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=?

2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=?
2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2
=2(lg根号下2)^2+1/2*lg2*lg5+根号下[(lg根号下2)^2-2*lg根号2+1]
=2(1/2*lg2)^2+1/2*lg2*lg5+根号下[(1/2*lg2)^2-lg2+1]
=2(1/2*lg2)^2+1/2*lg2*lg5+根号下[(1-1/2*lg2)^2]
=2(1/2*lg2)^2+1/2*lg2*lg5+(1-1/2*lg2)
=1/2*(lg2)^2+1/2*lg2*lg5-1/2lg2+1
=1/2*(lg2)^2+1/2*lg2*(lg5-1)+1
=1/2*(lg2)^2+1/2*lg2*(-lg2)+1
=1/2*(lg2)^2-1/2*(lg2)^2+1
=1

2(lg根号2)^2+1/2lg2*lg5+根号下(lg根号2-1)^2=2*(1/2lg2)²+1/2lg2*lg5+√(lg√2-1)²=
1/2(lg2)²+1/2lg2*lg5+lg√2-1=1/2lg2(lg2+lg5)+1/2lg2-1=1/2lg2+1/2lg2-1=lg2-1