一、等式与不等式的转化例1若正数a,b满足ab=a+b+3,则ab的取值范围是______.分析为了求ab的取值范围,只要将原等式转化为不等式即可.解运用不等式a+b≥2ab姨,原等式可化为不等式.∵ab=a+b+3≥2ab姨+3,∴ab-2ab姨-3≥0.又ab姨0,∴ab姨≥3,即ab≥9.例2已知不等式a2+b2+c2+4≤ab+ First, the transformation of equations and inequalities Example 1 If the positive number a, b satisfies ab = a + b + 3, then the range of ab is ______. Analysis In order to find the value range of ab, as long as the original equation is converted Inequality can be used to solve the inequality a + b ≥ 2ab 姨, the original equation can be turned into inequalities. ∵ ab = a + b + 3 ≥ 2ab 姨 +3, ∴ ab-2ab 姨 -3 ≥ 0. And ab 姨0, ∴ab姨≥3, ie ab≥9. Example 2 The known inequality a2+b2+c2+4≤ab+