Question

The solutions to the quadratic equation ${(x-1)}^2=\frac{4}{9}$ are

• A. $x=-\frac{5}{3},x=\frac{5}{3}$
• B. $x=\frac{1}{3},x=\frac{5}{3}$
• C. $x=\frac{5}{9},x=\frac{13}{9}$
• D. $x=1\pm \sqrt{\frac{2}{3}}$

Answer 1

Answer: (B)

$x=\frac{1}{3},x=\frac{5}{3}$

Given equation is $(x-1{)}^2=\frac{4}{9}$

Taking square root on both the sides, we get,
$x-1=\sqrt{\frac{4}{9}}$
$x-1=\pm \frac{2}{3}$
So, $x=1+\frac{2}{3}=\frac{5}{3}$ or $x=1-\frac{2}{3}=\frac{1}{3}$

$\therefore x=\frac{5}{3},x=\frac{1}{3}$