Question

Bài 1: Tìm số x,y,z biết x + y + z + 11 = 2\(\sqrt{x}+4\sqrt{y-1}+6\sqrt{z-2}\)

Bài 2: Tìm GTNN Q= \(\sqrt{x^2+4x+4}+\sqrt{x^2-4x+4}\)

Bài 3: Tìm GTLN P = \(\sqrt{x-2}+\sqrt{x-3}\) biết x+y = 6

Answer 1

Bài 1: \(x+y+z+11=2\sqrt{x}+4\sqrt{y-1}+6\sqrt{z-2}\)

ĐKXĐ:\(x\ge0;y\ge1;z\ge2\)

\(\Leftrightarrow x-2\sqrt{x}+1+\left(y-1\right)-2\cdot\sqrt{y-1}\cdot2+4+\left(z-2\right)-2\cdot\sqrt{z-2}\cdot3+9=0\)\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-2\right)^2+\left(\sqrt{z-2}-3\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=1\\\sqrt{y-1}=2\\\sqrt{z-2}=3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\y=5\\z=11\end{matrix}\right.\)

Answer 2

Bài 2: 

Q=|x+2|+|x-2|>=|x+2+2-x|=4

Dấu = xảy ra khi (x+2)(x-2)<=0

=>-2<=x<=2