Given:
An equation is given as
[tex]\sqrt{x+3}=x-3[/tex]
Find:
we have to solve the given equation for value of x.
Explanation:
we will solve the given equation as following
[tex]\begin{gathered} \sqrt{x+3}=x-3 \\ squaring\text{ both sides, we get} \\ x+3=x^2+9-6x \\ x^2-6x-x+9-3=0 \\ x^2-7x+6=0 \\ x^2-6x-x+6=0 \\ x(x-6)-1(x-6)=0 \\ (x-6)(x-1)=0 \\ x=6,1 \end{gathered}[/tex]
Now we will verify the solutions as
when x = 6
[tex]\begin{gathered} \sqrt{6+3}=6-3 \\ \sqrt{9}=3 \\ 3=3 \end{gathered}[/tex]
Therefore, x = 6 is the solution of given equation.
When x = 1
[tex]\begin{gathered} \sqrt{1+3}=1-3 \\ \sqrt{4}=-2 \\ 2\ne-2 \end{gathered}[/tex]
Therefore, x = 6 is the true solution of given equation.
Therefore, correct option is A, i.e. x = 6
