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均值不等式是高中数学中一个重要的不等式,它在证明不等式与求最值时十分有用.但同学们在使用均值不等式时,由于各种原因,会犯这样那样的错误.下面我们分类例析.错误一:忽视各项为正数而致误例11已知x∈R,求函数y=x+1/x的值域.错解:由x+1/x≥2得,函数y的值域为[2,+∞).剖析:错误的原因是想当然地把x看成了正数,在利用均值不等式求最值时,首先弄清所给的数是否为正,如果为负值,必须先变为正值,才能利用均值不等式.
Means inequality is an important inequality in high school mathematics, which is very useful in proving inequality and finding the most value, but when students use mean inequality, they will make such a mistake because of various reasons. Error 1: ignoring the positive result of each example 11 Known x∈R, find the value of the function y = x + 1 / x. Misinterpretation: from x + 1 / x ≥ 2, the value of the function y Domain is [2, + ∞) Analysis: The reason for the error is to take as a matter of course x as a positive value, the use of mean inequality for the most value, the first to find out whether the number given is positive, if it is negative, You must change to positive before you can use the mean inequality.