高中教材中基本不等式a+b2 ≥ab(a0 ,b 0 )是证明不等式时经常要用到的 ,等号成立的条件是“a=b” .若对a +b =P(定值 )当且仅当a =b=P2 (定值 )时 ,ab才取得最大值 .利用这一结论 ,我们可以证明一类不等式 :例 1　已知a、b都是正数 ,且a +b =1,求证 :　　　a+1+b+1≤ 6.证明 The basic inequalities a+b2 ≥ab(a0,b0) in high school textbooks are often used to prove inequalities, and the condition of the equal sign is “a=b”. If a +b = P (fixed value) And only when a = b = P2 (fixed value), ab gets the maximum value. Using this result, we can prove a type of inequality: Example 1 Know that a, b are positive, and a +b =1, Proof: a+1+b+1≤ 6. Proof