\(a^2+b^2+c^2+d^2+e^2\ge ab+ac+ad+ae\)
Ta có :
\(a^2+b^2+c^2+d^2+e^2\)
\(=\left(\dfrac{a^2}{4}+b^2\right)+\left(\dfrac{a^2}{4}+c^2\right)+\left(\dfrac{a^2}{4}+d^2\right)+\left(\dfrac{a^2}{4}+e^2\right)\)
Ta lại có :
\(\left(\dfrac{a}{2}-b\right)^2\ge0\Leftrightarrow\) \(\dfrac{a^2}{4}-ab+b^2\ge0\) \(\dfrac{\Rightarrow a^2}{4}+b^2\ge ab\)
Tương tự :
\(\dfrac{a^2}{4}+c^2\ge ac\)
\(\dfrac{a^2}{4}+d^2\ge ad\)
\(\dfrac{a^2}{4}+e^2\ge ae\)
\(\Rightarrow\left(\dfrac{a^2}{4}+b^2\right)+\left(\dfrac{a^2}{4}+c^2\right)+\left(\dfrac{a^2}{4}+d^2\right)+\left(\dfrac{a^2}{4}+e^2\right)\ge ab+ac+ad+ae\)
\(\Rightarrow a^2+b^2+c^2+d^2+e^2\ge ab+ac+ad+ae\)
