Question

tìm x,y,z biết

x+y+z+35=\(2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x\ge-1\\y\ge-2\\z\ge-3\end{matrix}\right.\)

x+y+z+35=\(4\sqrt{x+1}+6\sqrt{y+2}+8\sqrt{z+3}\)

\(\Leftrightarrow\left(x+1-2.2\sqrt{x+1}+4\right)+\left(y+2-2.3\sqrt{y+2}+9\right)+\left(z+3-2.4\sqrt{z+3}+16\right)=0\)

\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{y+2}-3\right)^2+\left(\sqrt{z+3}-4\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x+1}-2\right)^2=0\\\left(\sqrt{y+2}-3^{ }\right)^2=0\\\left(\sqrt{z+3}-4\right)^2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=7\\z=13\end{matrix}\right.\)