\(x^2+y^2+z^2-x-y-z+0,75=0\)
\(\Leftrightarrow x^2+y^2+z^2-x-y-z+\frac{3}{4}=0\)
\(\Leftrightarrow\left(x^2-x+\frac{1}{4}\right)+\left(y^2-y+\frac{1}{4}\right)+\left(z^2-z+\frac{1}{4}\right)=0\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{2}\right)^2+\left(z-\frac{1}{2}\right)^2=0\)
Dễ thấy: \(\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{2}\right)^2+\left(z-\frac{1}{2}\right)^2\ge0\)
Xảy ra khi \(\hept{\begin{cases}x-\frac{1}{2}=0\\y-\frac{1}{2}=0\\z-\frac{1}{2}=0\end{cases}}\)\(\hept{\begin{cases}x-\frac{1}{2}=0\\y-\frac{1}{2}=0\\z-\frac{1}{2}=0\end{cases}}\)
Đúng 0
Bình luận (0)
