1．2(lg√2)²+(lg√2)(lg5)+√[(lg√2)²-lg2+1]
=(lg√2)[2(lg√2)+lg5]+√[(lg√2)²-2(lg√2)+1]
=(lg√2) (lg2+lg5)+√[(lg√2)-1]²
=(lg√2)+| (lg√2)-1|
=(lg√2)+1- (lg√2)
=1；
2．∵(3+2√2)(3-2√2)=1,
∴3+2√2=1/(3-2√2)= (3-2√2)^(-1)
log<(3-2√2)>(3+2√2)
= log<(3-2√2)>[(3-2√2)^(-1)]
= -1.