数学题,要用基本不等式解,大家帮帮忙!
已知正数a,b满足ab=2a+b+3,求a+b的最小值
(写明过程,谢谢)
参考答案:ab - 2a - b - 3
= ( ab - 2a - b + 2 ) - 5
= (a - 1)(b - 2) - 5
= 0
所以:
(a - 1)(b - 2) = 5
所以:
a + b
= (a-1) + (b-2) + 3
>= 2√((a-1)(b-2)) + 3
= 2√5 + 3
已知正数a,b满足ab=2a+b+3,求a+b的最小值
(写明过程,谢谢)
参考答案:ab - 2a - b - 3
= ( ab - 2a - b + 2 ) - 5
= (a - 1)(b - 2) - 5
= 0
所以:
(a - 1)(b - 2) = 5
所以:
a + b
= (a-1) + (b-2) + 3
>= 2√((a-1)(b-2)) + 3
= 2√5 + 3