Question

(2x - 1) ^ 2 - 1/4 = 2

Answer 1

\(\left(2x-1\right)^2-\dfrac{1}{4}=2\)

\(\Leftrightarrow\left(2x-1\right)^2=2+\dfrac{1}{4}\)

\(\Leftrightarrow\left(2x-1\right)^2=\dfrac{9}{4}\)

\(\Leftrightarrow\left(2x-1\right)^2=\left(\dfrac{3}{2}\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=\dfrac{3}{2}\\2x-1=-\dfrac{3}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{5}{2}\\2x=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

Answer 2

(2x - 1)² - 1/4 = 2

→ (2x - 1)² = 8/4 + 1/4

→ (2x - 1)² = 9/4

→ 2x - 1 = 3/2 hoặc 2x - 1 = -3/2

→ 2x = 3/2 + 1 = 5/2 hoặc 2x = -3/2 + 1 = -1/2

→ x = 5/2 ÷ 2 hoặc x = -1/2 ÷ 2

→ x = 5/4 hoặc x = -1/4