a2+1/ab+1/a(a-b)= ab+1/ab+a(a-b)+1/a(a-b)≥4
当且仅当 ab=1/ab,a(a-b)=1/a(a-b)取等号
即 a=√2,b=√2/2取等号．
∴ a2+1/ab+1/a(a-b)的最小值为4