Question

(1-2x)²-\(3|2x-1|\)=0

Answer 1

(1-2x)² - 3|2x-1| = 0

=> (1-2x)(1-2x) - 3|2x-1|=0

=> (1-2x)-(2x-4x) - 3|2x-1| = 0

=> 1 - 3|2x-1| = 0

=> 3|2x-1|=1

=> |2x-1|= 1/3

=> 2x-1 \(\in\){1/3; -1/3}

=> x \(\in\){2/3; 1/3}

Answer 2

\(\left(1-2x\right)^2=3\left|2x-1\right|\)

TH1: \(2x-1< 0\)⇔\(x< \frac{1}{2}\)

⇒ \(\left|2x-1\right|=1-2x\)

⇒ \(\left(1-2x\right)^2=3\left(1-2x\right)\)

\(1-2x=3\)

\(x=\frac{1-3}{2}=-1\)( thỏa mãn)

TH2:\(\) 2x-1 ≥ 0 ⇔ x ≥ \(\frac{1}{2}\)

⇒\(\left|2x-1\right|=2x-1\)

\(\left(1-2x\right)^2=\left(2x-1\right)^2\)

\(\left(2x-1\right)^2=3\left(2x-1\right)\)

\(2x-1=3\)

\(x=\frac{3+1}{2}=\frac{4}{2}=2\)(thỏa mãn)

Vậy x=2 hoặc -1