基本不等式(ab)~(1/2)≤(a+b)/2(a≥0,b≥0)常用于证明不等式以及求某些函数的最大值或最小值。设a,b均为正实数,a+b=s,ab=t,当s为定值时,t取到最大值s~2/4;当t为定值时,s取到最小值2t~(1/2)。利用基本不等式求函数最值或值域等问题时,必须满足三个条件:一正、二定、三相等、这三个条件缺一不可,否则就会导致错误。 The basic inequality (ab) ~ (1/2) ≤ (a + b) / 2 (a ≥ 0, b ≥ 0) is often used to prove the inequality and find the maximum or minimum of some functions. Suppose a, b are positive real numbers, a + b = s, ab = t, when s is constant, t takes the maximum value s ~ 2/4; when t is fixed value, s takes the minimum value 2t ~ (1/2). The use of basic inequalities to find the value of the function or range and other issues, we must meet three conditions: one positive, two fixed, three equal, these three conditions are indispensable, otherwise it will lead to errors.