Question

If $\sqrt{x}+6=x$, then find the value of $x$.

• A. $4$ only
• B. $9$ only
• C. $4$ or $9$
• D. $-4$ or $9$
• E. There is no solution

Answer 1

The correct option is B $9$ only

Given, $\sqrt{x}+6=x$

$\Rightarrow \sqrt{x}=x-6$

Now squaring both the sides, we get
$\Rightarrow x=x^2-12x+36$

$\Rightarrow x^2-13x+36=0$

$\Rightarrow x^2-9x-4x+36=0$

$\Rightarrow (x-9)(x-4)=0$
The solutions are $4$ and $9$, but for $x=4$, the original equation wont be satisfied.
So, the correct answer is $x=9$.