Question

giải bpt

a) /x²+3/>5x-2

b) /\(\dfrac{2x}{x+3}-1\)/>2

dấu /.../ là giá tri tuỵet đối

Answer 1

a: \(\Leftrightarrow x^2+3>5x-2\)

\(\Leftrightarrow x^2-5x+5>0\)

\(\Leftrightarrow x\in\left(-\infty;\dfrac{5-\sqrt{5}}{2}\right)\cup\left(\dfrac{5+\sqrt{5}}{2};+\infty\right)\)

b: \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2x}{x+3}-1>2\\\dfrac{2x}{x+3}-1< -2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{2x-3\left(x+3\right)}{x+3}>0\\\dfrac{2x+x+3}{x+3}< 0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x+9}{x+3}< 0\\\dfrac{x+1}{x+3}< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-9< x< -3\\-3< x< -1\end{matrix}\right.\)