Question

giải phương trình

(x-1)(4-x)≥ x(x-3)-2x²

^{\(\dfrac{x+2}{x-5}-3< 0\)}

Answer 1

\(\dfrac{x+2}{x-5}-3< 0\)

\(\Leftrightarrow\dfrac{x+2-3\left(x-5\right)}{x-5}< 0\)

\(\Leftrightarrow x+2-3x+15< 0\)

\(\Leftrightarrow-2x+17< 0\)

\(\Leftrightarrow-2x< -17\)

\(\Leftrightarrow x>\dfrac{17}{2}\)

Answer 2

\(\left(x-1\right)\left(4-x\right)\ge x\left(x-3\right)-2x^2\)

\(\Leftrightarrow4x-x^2-4+x-x^2+3x+2x^2\ge0\)

\(\Leftrightarrow8x-4\ge0\)

\(\Leftrightarrow4\left(2x-1\right)\ge0\)

\(\Leftrightarrow2x-1\ge0\)

\(\Leftrightarrow2x\ge1\)

\(\Leftrightarrow x\ge\dfrac{1}{2}\)