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对称式的最值问题是高中数学不等式板块的主流问题,绝大多数题目都是在变量相等时取得最值,但是一切都有例外,请看下面的例子.例1设x,y为实数,且x+y=6,求f(x,y)=(x2+4)(y2+4)的最小值.分析本题x,y非常对称,按照对称原理猜测x=y=3时目标函数取得最小值,其最小值为f(3,3)=169,真的如此吗?f(0,6)=160<169,f(7,-1)=265>169,可见f(3,3)既不是最大
Symmetry of the most value problem is the mainstream of high school mathematics inequality plate, the vast majority of topics are obtained when the variables are equal, but everything has an exception, see the following example.Example 1 Let x, y is a real number, And x + y = 6, find the minimum value of f (x, y) = (x2 + 4) (y2 + 4) .Analysis of the problem x, y is very symmetrical, according to the symmetry principle guess x = y = 3 when the objective function F (0,6) = 160 <169, f (7, -1) = 265> 169, we can see that f (3, 3) Neither is the biggest