Question

设a>0,b>0,a+b=1,求证:1/a+1/b+1/a*b>=8(用综合法、分析法两种方法证明)

Answer 1

a+b=1
a+b≥2√ab
所以
2√ab≤1
4ab≤1
ab≤1/4
1/ab≥4
1/a + 1/b + 1/ab
=(a+b)/ab+1/ab
=1/ab+1/ab
=2/ab
≥2*4=8