Question

A=\(\sqrt{\left(3x-5\right)\left(4x+7\right)}\)

tìm x để A có nghĩa

Answer 1

Để A có nghĩa thì (3x-5)(4x+7) \(\ge\)0

=> \(\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-5\ge0\\4x+7\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-5\le0\\4x+7\le0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{5}{3}\\x\ge\dfrac{-7}{4}\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{5}{3}\\x\le\dfrac{-7}{4}\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x\ge\dfrac{5}{3}\\x\le\dfrac{-7}{4}\end{matrix}\right.\)

Vậy x\(\ge\dfrac{5}{3}\) hoặc x\(\le\dfrac{-7}{4}\)