高一数学对数题,谁来帮帮忙若lga,lgb是方程2x^2-4+1=0的两个实数,求lg(ab)(lga/b)^2的值

Question

高一数学对数题,谁来帮帮忙
若lga,lgb是方程2x^2-4+1=0的两个实数,求lg(ab)(lga/b)^2的值

Answer 1

log(ab)lg(a/b)^2
=log(ab)(log a^2 - log b^2)
=log(ab+a^2)-log(ab+b^2)
=log((ab+a^2)/(ab+b^2))
=log(a/b)
=log a - log b
从方程得出,
log a + log b =2
log a * log b =1/2
(log a - log b)^2 =(log a +log b)^2-4*log a * log b
=4-2=2
所以log a - log b = 根号2
所以log(ab)log(a/b)^2 = 根号2