Question

What is the solution to the equation below?A.x = 6B.x = 3C.x = 1D.x = 4

Answer 1

Given:

An equation is given as

`√(x+3)=x-3`

Find:

we have to solve the given equation for value of x.

Step-by-step explanation:

we will solve the given equation as following

`\begin{gathered} √(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}`

Now we will verify the solutions as

when x = 6

`\begin{gathered} √(6+3)=6-3 \\ √(9)=3 \\ 3=3 \end{gathered}`

Therefore, x = 6 is the solution of given equation.

When x = 1

`\begin{gathered} √(1+3)=1-3 \\ √(4)=-2 \\ 2\\e-2 \end{gathered}`

Therefore, x = 6 is the true solution of given equation.

Therefore, correct option is A, i.e. x = 6