Question

Câu 1: Rút gọn các biểu thức sau:

a. \(\sqrt{36\left(x-5\right)^2}\) với x ≥ 5

b. \(\sqrt{\dfrac{1}{4}\left(1-x\right)^2}\) với x > 1

c. \(\sqrt{x^2\left(2x-4\right)^2}\) với a ≥ 2

d. \(\dfrac{1}{x}\sqrt{x^2\left(1+x\right)^2}\) với x < -1

Answer 1

a) \(\sqrt{36\left(x-5\right)^2}\left(x\ge5\right)=6\left|x-5\right|=6\left(x-5\right)=6x-30\)

b) \(\sqrt{\dfrac{1}{4}\left(1-x\right)^2}\left(x>1\right)=\dfrac{1}{2}\left|1-x\right|=\dfrac{1}{2}\left(x-1\right)=\dfrac{1}{2}x-\dfrac{1}{2}\)

c) \(\sqrt{x^2\left(2x-4\right)^2}\left(x\ge2\right)=\left|x\left(2x-4\right)\right|=x\left(2x-4\right)=2x^2-4x\)

d) \(\dfrac{1}{x}\sqrt{x^2\left(1+x\right)^2}\left(x< -1\right)=\dfrac{1}{x}\left|x\left(1+x\right)\right|=\dfrac{1}{x}x\left(1+x\right)=1+x\)