Question

1, Tìm Min của

A = \(\sqrt{4x^2-4x+1}+\sqrt{4x^2-12x+9}\)

2, Tìm x,y,z biết

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

Giúp em với ạ em đang cần gấp!!!!

Answer 1

\(A=\sqrt{\left(2x-1\right)^2}+\sqrt{\left(2x-3\right)^2}\)

\(A=\left|2x-1\right|+\left|3-2x\right|\ge\left|2x-1+3-2x\right|=2\)

\(A_{min}=2\) khi \(\left(2x-1\right)\left(3-2x\right)\ge0\Leftrightarrow\frac{1}{2}\le x\le\frac{3}{2}\)

2. ĐKXĐ: ...

\(\Leftrightarrow x-1-2\sqrt{x-1}+1+\left(y-2-4\sqrt{y-2}+4\right)+\left(z-3-6\sqrt{z-3}+9\right)=0\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}-1=0\\\sqrt{y-2}-2=0\\\sqrt{z-3}-3=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=6\\z=12\end{matrix}\right.\)