关于基本不等式已知a,b为正实数,且a+b=1,求证：ab+1/ab≥17/4

Question

关于基本不等式
已知a,b为正实数,且a+b=1,求证：ab+1/ab≥17/4

Answer 1

a>0,b>0,a+b=1
ab≤[(a+b)/2]^2=1/4
ab+1/ab=ab+1/16ab+15/16ab
≥2√ab*1/16ab+15/16ab
≥1/2+15/16*4=17/4
ab+1/ab≥17/4