1.基本不等式
<span class="equation-text" data-index="0" data-equation="a \in R ，a^2 \geq 0 , \left| a\right| \geq 0" contenteditable="false"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="\frac{a^2 + b^2}{2} = (\frac{a + b}{2})^2"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="a^2+b^2+c^2 \geq ab + bc + ac"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="若a > b > 0 ，m > 0 ，则 \frac{b}{a} < \frac{b + m}{a + m}"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="若a,b同号且a>b 则 \frac{1}{a} < \frac{1}{b}"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="a,b\in R ,则 a^2 + b^2 \geq 2ab"><span></span><span></span></span>， 当且仅当a=b时取“=”
<span class="equation-text" contenteditable="false" data-index="0" data-equation="a> 0,b >0 ,a+b\geq 2\sqrt{ab},当且仅当 a = b时取“=”"><span></span><span></span></span>
2.均值不等式
两个正数的均值不等式：<span class="equation-text" contenteditable="false" data-index="0" data-equation="\frac{a + b}{2} \geq \sqrt{ab} 变形 a+ b \geq 2\sqrt{ab},ab \leq (\frac{a + b}{2})^2 等"><span></span><span></span></span>
3.最值定理
设<span class="equation-text" contenteditable="false" data-index="0" data-equation="x,y>0,由x+y\geq 2\sqrt{xy}"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="1.如果x,y是正数，且积xy = P (是定值)，则x=y时，x,y的和x+y有最小值2\sqrt{P}"><span></span><span></span></span>
<span class="equation-text" contenteditable="false" data-index="0" data-equation="2.如果x,y是正数，且和x+y=S(是定值)，则x=y时，x,y的积xy有最大值 (\frac{S}{2} )^2"><span></span><span></span></span>
运用最值定理求最值的三要素：一正二定三相等
三要素
4.利用均值不等式可以证明不等式，求最值、取值范围、比较大小等
例题1
