\(a^2+b^2+c^2+d^2=a(b+c+d)\)
\(\Leftrightarrow 4a^2+4b^2+4c^2+4d^2=4ab+4ac+4ad\)
\(\Leftrightarrow a^2+(a^2-4ab+4b^2)+(a^2-4ac+4c^2)+(a^2-4ad+4d^2)=0\)
\(\Leftrightarrow a^2+(a-2b)^2+(a-2c)^2+(a-2d)^2=0\)
Mà \(\left\{\begin{matrix}
a^2 \ge0\\ (a-2b)^2 \ge0
\\ (a-2c)^2 \ge0
\\ (a-2d)^2 \ge0
\end{matrix}\right.\)
\(\Rightarrow \left\{\begin{matrix}
a^2 =0\\ (a-2b)^2 =0
\\ (a-2c)^2 =0
\\ (a-2d)^2 =0
\end{matrix}\right.
\Leftrightarrow \left\{\begin{matrix}
a =0\\ a-2b =0
\\ a-2c =0
\\ a-2d=0
\end{matrix}\right.
\Leftrightarrow a=b=c=d=0\)
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