Question

Giải bpt

\(\frac{9}{\left|x-5\right|-3}\ge\left|x-2\right|\)

Answer 1

ĐKXĐ:...

Xét \(x\le2\)

\(\Rightarrow\frac{9}{5-x-3}\ge2-x\Leftrightarrow9\ge4-4x+x^2\)

\(\Leftrightarrow x^2-4x-5\le0\Leftrightarrow-1\le x\le5\)

\(\Rightarrow-1\le x\le2\)

Xét \(2< x\le5\)

\(\Rightarrow\frac{9}{2-x}\ge x-2\Leftrightarrow9\ge-x^2+4x-4\Leftrightarrow x^2-4x+13\ge0\)

=> \(2< x\le5\)

Xét \(x< 5\)

\(\Rightarrow\frac{9}{x-8}\ge x-2\Leftrightarrow9\ge x^2-10x+16\Leftrightarrow x^2-10x+7\le0\)

\(\Rightarrow5-3\sqrt{2}\le x\le5+3\sqrt{2}\)

\(\Rightarrow5-3\sqrt{2}\le x< 5\)