数学不等式的求证题已知a＞=3,求证 a^1/2 - (a-1)^1/2 ＜ (a-2)^1/2- (a-1)^1/2
问题描述：
数学不等式的求证题
已知a＞=3,求证 a^1/2 - (a-1)^1/2 ＜ (a-2)^1/2- (a-1)^1/2
答
（√a+√(a-2))^2-(2√(a-1))^2
=[2a-2+2√a(a-2)]-(4a-4)
=2(√a(a-2)-(a-1))
(√a(a-2))^2-(a-1)^2
=(a^2-2a)-(a^2-2a+1)
=-1
所以,√a(a-2)-(a-1)（√a+√(a-2))^2-(2√(a-1))^2√a+√(a-2) a^1/2 - (a-1)^1/2 ＜ (a-1)^1/2- (a-2)^1/2