Question

如果正数a、b满足ab-(a+b)=1,则ab的最小值是

Answer 1

ab-(a+b)=1

b=(a+1)/(a-1)

则ab=a*(a+1)/(a-1)

=(a^2+a)/(a-1)

=a+2+2/(a-1)

=3+(a-1)+2/(a-1)

≥3+2√[(a-1)*2/(a-1)]

=3+2√2

所以ab的最小值是3+2√2