在基本不等式的应用中,重要不等式a2+b2≥2ab往往起着关键的作用,尤其是它的两种变式在处理某些不等式问题中有着意想不到的效果.变式一a2+b2≥2|ab|.由a2+b2=|a|2+|b|2≥2|ab|得a2+b2≥2|a·b|(当且仅当|a|=|b|时等号成立),这一变式轻易地实现了将实数转化为非负数的目的,在解题中有时也非常有用.例1如果实数x、y满足x2+y2=1,则(1 In the application of basic inequality, the important inequality a2 + b2≥2ab often plays a key role, especially its two variants have an unexpected effect in dealing with some inequalities. Variant a2 + b2≥2 | ai | a | b | is given by a2 + b2 = | a | 2+ | b | 2 ≧ 2 | ab | a2 + b2 ≧ 2 | a · b | (Equivalent holds if and only if | a | = | b | ) This variant easily achieves the purpose of converting a real number to a nonnegative number, sometimes useful in solving problems. Example 1 If the real number x, y satisfies x2 + y2 = 1, then (1