Question

1/ Tìm x, y, z. Biết

 ( x + y - z )² + ( x - y + 6 )² + ( z + 2 )² = 324

 

Answer 1

     \(\left(x+y-z\right)^2+\left(x-y+6\right)^2+\left(z+2\right)^2=0\)

Đánh giá:   \(\left(x+y-z\right)^2\ge0;\)\(\left(x-y+6\right)^2\ge0;\)\(\left(z+2\right)^2\ge0\)

\(\Rightarrow\)\(\left(x+y-z\right)^2+\left(x-y+6\right)^2+\left(z+2\right)^2\ge0\)

Dấu  "="  xảy ra   \(\Leftrightarrow\)\(\hept{\begin{cases}x+y-z=0\\x-y+6=0\\z+2=0\end{cases}}\)\(\Leftrightarrow\)\(\hept{\begin{cases}x=5\\y=-7\\z=-2\end{cases}}\)

Vậy....

Answer 2

\(\hept{\begin{cases}x+y-z=0\\x-y+6=0\\z+2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-4\\y=2\\z=-2\end{cases}}}\)