( lg√2 )^2+1/2lg2lg5+√(lg√2)^2 -lg2+1
1个回答

(lg√2)^2+(1/2)(lg2)(lg5)+√[(lg√2)^2-lg2+1]

=(lg√2)^2+lg[2^(1/2)]*lg5+√{(lg√2)^2-lg[(√2)^2]+1}

=(lg√2)^2+lg(√2)*lg5+√[(lg√2)^2-2(lg√2)+1]

=(lg√2)^2+lg(√2)*lg5+√[(lg√2 -1)^2]

=(lg√2)^2+lg(√2)*lg5+[1-lg√2]

=(lg√2)[lg√2+lg5-1] +1

=(lg√2)[lg√2+lg(5/10)]+1

=(lg√2)[lg(√2/2)]+1

=(lg√2)[lg(1/√2)]+1

=1-(lg√2)^2