\(a^2+b^2+c^2+d^2+e^2=a\left(b+c+d+e\right)\)
\(4a^2+4b^2+4c^2+4d^2+4e^2=4a\left(b+c+d+e\right)\)
\(\left(a^2-4ab+4b^2\right)+\left(a^2-4ac+4c^2\right)+\left(a^2-4ad+4d^2\right)+\left(a^2-4ae+4e^2\right)=0\)
\(\left(a-2b\right)^2+\left(a-2c\right)^2+\left(a-2d\right)^2+\left(a-2e\right)^2=0\)
Do \(\left\{{}\begin{matrix}\left(a-2b\right)^2\ge0\\\left(a-2c\right)^2\ge0\\\left(a-2d\right)^2\ge0\\\left(a-2e\right)^2\ge0\end{matrix}\right.\); \(\forall a;b;c;d;e\)
\(\Rightarrow\left(a-2b\right)^2+\left(a-2c\right)^2+\left(a-2d\right)^2+\left(a-2e\right)^2\ge0\)
Dấu "=" xảy ra khi và chỉ khi:
\(\left\{{}\begin{matrix}a-2b=0\\a-2c=0\\a-2d=0\\a-2e=0\end{matrix}\right.\) \(\Rightarrow a=2b=2c=2d=2e\)
\(\Rightarrow b=c=d=e\)
