Question

Rút gọn biểu thức:

A=6x+\(\sqrt{9x^2-12x+4}\)

B=5x-\(\sqrt{x^2+4x+4}\)

Answer 1

+) ta có : \(A=6x+\sqrt{9x^2-12x+4}=6x+\sqrt{\left(3x-2\right)^2}\)

\(=6x+\left|3x-2\right|\) \(\Rightarrow\left[{}\begin{matrix}A=9x-2\left(x\ge\dfrac{2}{3}\right)\\A=3x+2\left(x< \dfrac{3}{2}\right)\end{matrix}\right.\)

+) ta có : \(B=5x-\sqrt{x^2+4x+4}=5x-\sqrt{\left(x+2\right)^2}\)

\(=5x-\left|x+2\right|\) \(\Rightarrow\left[{}\begin{matrix}A=4x-2\left(x\ge-2\right)\\6x+2\left(x< -2\right)\end{matrix}\right.\)