Solve for x if \$\sqrt("x" + 3) - \sqrt("x") = 3\$.

The given equation is

\$\sqrt("x" + 3) - \sqrt("x") = 3\$

To solve this equation, let’s first isolate one of the square roots. We’ll isolate \$\sqrt("x")\$ by adding \$\sqrt("x")\$ to both sides:

\$\sqrt("x" + 3) - \sqrt("x") + \sqrt("x") = 3 + \sqrt("x")\$

Now, let’s square both sides to eliminate the square roots:

\$(\sqrt("x" + 3))^2 = (3 + \sqrt("x"))^2\$

\$(("a" + "b")^2 = "a"^2 + 2"ab" + "b"^2)\$

Simplify the equation

x + 3 = 9 + \$ 2 times 3 times \sqrt("x")\$ + x

x + 3 = 9 + \$6 \sqrt("x")\$ + x

Then move constant terms to one side and x terms to another side

x - x - \$6\sqrt("x")\$ = 9 - 3

\$- 6\ sqrt("x") = 6\$

\$\sqrt("x") = - 6/6\$

\$\sqrt("x") = - 1\$

Square both sides to solve for x:

\$(\sqrt("x"))^2 = (- 1)^2\$

x = 1

So, the solution is x = 1.

Option A is incorrect because the solution for x does not equal 3

3

Incorrect since the value of x does not equate to 2 in the solution

2

Option C is inaccurate as the solution for x is not 4, as stated

4

Hence, the accurate solution is option D, where x equals 1

1

Option

D

Can you summarize what you’ve understood in the above steps?