Question

Roots of the equation $x^2-6x-\sqrt{x^2-6x-3}=5$ are

• A. $1,7$
• B. $-1,-7$
• C. $1$, $-1$
• D. $-1$, $7$

Answer 1

The correct option is D $-1$, $7$

$x^2-6x-5=\sqrt{x^2-6x-3}$
Squaring on both sides.
$(x^2-6x-5{)}^2=x^2-6x-3.$
$x^4+36x^2+25-12x^3+60x-10x^2=x^2-6x-3$
$x^4-12x^3+25x^2+66x+28=0.$
$x=-1,7$ satisfies above equation .
Also, $x^2-6x-3\ge 0forx=-1,7$
$\Rightarrow x=-1,7$ are the roots .