Question

The roots of the quadratic equation
$x^2-.2ax+a^2+b^2-c^2=0$ are where a,b,c $\in R:$

Answer 1

$x^2-2ax+a^2=c^2-b^2$

$\Rightarrow {(x-a)}^2=c^2-b^2$

$\Rightarrow x-a=\pm \sqrt{c^2-b^2}$

$\Rightarrow x=a\pm \sqrt{c^2-b^2}$

$\therefore x=\{a+\sqrt{c^2-b^2},a-\sqrt{c^2-b^2}\}$