Question

Tìm x,y,z,t thỏa mãn: x²+y²+z²+t²=x.(y+z+t)

Answer 1

\(x^2+y^2+z^2+t^2=x\left(y+z+t\right)\)

\(\Rightarrow4x^2+4y^2+4z^2+4t^2=4xy+4xz+4xt\)

\(\Rightarrow4x^2+4y^2+4z^2+4t^2-4xy-4xz-4xt=0\)

\(\Rightarrow x^2-4xy+4y^2+x^2-4xz+4z^2+x^2-4xt+4t^2+x^2=0\)

\(\Rightarrow\left(x-2y\right)^2+\left(x-2z\right)^2+\left(x-2t\right)^2+x^2=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2y=0\\x-2z=0\\x-2t=0\\x=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=2y\\x=2z\\x=2t\\x=0\end{matrix}\right.\)

\(\Rightarrow x=y=z=t=0\)

Kết luận: \(x=y=z=t=0\)