Question

Tìm x,y,z thỏa mãn; \(\sqrt{\left(x-\sqrt{5}\right)^2}\)+\(\sqrt{\left(y+\sqrt{3}\right)^2}\)+ lx-y-zl=0

Answer 1

\(\sqrt{\left(x-\sqrt{5}\right)^2}+\sqrt{\left(y+\sqrt{3}\right)}+\left|x-y-z\right|=0\)

\(\Leftrightarrow\left|x-\sqrt{5}\right|+\left|y+\sqrt{3}\right|+\left|x-y-z\right|=0\)

Ta có \(\hept{\begin{cases}\left|x-\sqrt{5}\right|\ge0\\\left|y+\sqrt{3}\right|\ge0\\\left|x-y-z\right|\ge0\end{cases}}\)

=>  \(VT\ge0\)

Dấu = xảy ra khi

\(\hept{\begin{cases}x-\sqrt{5}=0\\y+\sqrt{3}=0\\x-y-z=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\sqrt{5}\\y=-\sqrt{3}\\z=\sqrt{5}+\sqrt{3}\end{cases}}\)