Question

Find the value of $x$ which satisfies the eqution $\sqrt{3-x}-x=3$

• A. $-1$ or $-6$
• B. $1$ or $-6$
• C. $-1$ only
• D. $-6$ only
• E. There is no solution

Answer 1

The correct option is C $-1$ only

Given, $\sqrt{3-x}-x=3$

$\Rightarrow \sqrt{3-x}=3+x$

Squaring on both the sides, we get
$3-x={(3+x)}^2=x^2+6x+9$
$\Rightarrow x^2+7x+6=0$

$\Rightarrow x=-1,-6$

But for $-6$ , the original given equation wont satisfy (check it)
So, the correct answer is $-1$.