Question

Bt : Rút gọn

a) \(\sqrt{\left(x-3\right)^2}\)

b) \(\sqrt{\left(3x+1\right)^2}+2x\) vs( x<1/3)

c) \(\sqrt{\left(1-2x\right)^2}+2x\) vs ( x>hoặc = 1/2 )

Answer 1

a)\(\sqrt{\left(x-3\right)^2}=|x-3|\)(*)

TH1: x-3 \(\ge0\Leftrightarrow x\ge3\)

(*)=> |x - 3|=x-3

TH2 \(x-3< 0\Leftrightarrow x< 3\)

(*)=>|x-3|=-(x-3)=3-x

Vậy khi x\(\ge\)3 thì (*)=x-3

Khi x<3 thì (*)=3-x

b) ĐK: x<\(\dfrac{1}{3}\)

\(\sqrt{\left(3x+1\right)^2}+2x\\ =\left|3x+1\right|+2x\left(@\right)\)

TH1:3x+1\(\ge\)0\(\Leftrightarrow3x\ge-1\Leftrightarrow x\ge-\dfrac{1}{3}\)=>\(-\dfrac{1}{3}\le x\le\dfrac{1}{3}\)

(@)=>|3x+1|+2x

=3x+1+2x

=5x+1

TH2 \(3x+1< 0\Leftrightarrow3x< -1\Leftrightarrow x< -\dfrac{1}{3}\)

(@)=>|3x+1|+2x

= -3x-1+2x

= -x-1

c) tương tự như vậy