(lg√2)^2+1/2lg2*lg5+√(lg√2)^-lg2+1 化简求值

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(lg√2)^2+1/2lg2*lg5+√(lg√2)^-lg2+1 化简求值

(lg√2)^2+1/2lg2*lg5+√(lg√2)^-lg2+1 化简求值
(lg√2)^2+1/2lg2*lg5+√(lg√2)^-lg2+1 化简求值

(lg√2)^2+1/2lg2*lg5+√(lg√2)^-lg2+1 化简求值
=lg(√2)^2+1/2lg2*lg5+√((lg√2)^2-lg2+1)
=lg2+1/2lg2*lg5+√((lg√2)^2-2lg√2+1)
=lg2+1/2lg2*lg5+√(lg√2-1)^2
=lg2+1/2lg2*lg5+|lg√2-1|
=lg2+1/2lg2*lg5+1-1/2lg2
=1/2lg2+1/2lg2*lg5+1
=1/2lg2+1/2lg2*lg5+1
=1/2lg2(1+lg5)+1
=1/2lg2(1+1-lg2)+1
=lg2-1/2(lg2)^2+1
=-1/2(lg2-1)^2+3/2
lg2 = 0.3010
所以原式=1.2557