\(\sqrt{2x + 2} −\sqrt{x − 3} = 2\)
\(\sqrt{2x + 2} = 2 + \sqrt{x − 3}\)

Let us remove the square roots first by squaring both sides;
\((2x + 2) = 4 + (x - 3) + 4\sqrt{x-3}\)
\(x + 1 = 4\sqrt{x-3}\)

Squaring again;
\(x^2 + 2x + 1 = 16(x - 3)\)
\(x^2 + 2x + 1 = 16x - 49\)
\(x^2 - 14x + 49 = 0\)

Using Middle-Term Splitting;
\(x^2 - 7x - 7x + 49 = 0\)
\(x(x - 7) - 7(x - 7) = 0\)
\((x - 7)(x - 7) = 0\)

i.e. only x =7 satisfies the given equation

Col. A: 7
Col. B: 7

Hence, option C