Question

若为正数a.b,ab=a+b+3.求ab的最小值,根号请用1/2次方表示

Answer 1

均值不等式为 a+b>=2*(ab)^(1/2)

ab=a+b+3>=2*(ab)^(1/2)+3

令t=（ab)^(1/2)>0

则有

t^2-2t+1>=4

(t-1)^2>=4

t-1>=2或<=-2

t>=3 (t<=-1舍去)

ab=t^2>=9

ab的最小值是9