√是根号
因为a+b=1
所以1/b=a+b/b=a/b+1
1/a=a+b/a=b/a+1
1/b+1/a=a/b+1 +b/a+1=a/b+b/a+2
根据其本不等式:
a/b+b/a+2≥2+2×√a/b×b/a
a/b+b/a+2≥2+2=4
√ab ≤ (a+b)/2 = 1/2, ab≤ (1/2)^2 = 1/4, 1/(ab)≥ 4
1/b+1/a = (a+b)/ab = 1/ab ≥ 4
1/b+1/a=(1/b+1/a)(a+b)
=2+a/b+b/a
≥2+2
=4