Question

Find the roots of the following quadratic equations (if they exist ) by the method of completing the square.
$x^2-4ax+4a^2-b^2=0$

Answer 1

$X^2-4aX+4a^2-b^2=0$

$X^2-4aX+4a^2=b^2$

$(X-2a)(X-2a)=b^2$

$\sqrt{(X-2a{)}^2}=\sqrt{b^2}$

$\Rightarrow X-2a=\pm b$

$X-2a\pm b=0$

$X=2a\pm b$

are the roots of equation.