Find the value
\[ x = \frac{2}{3 + \sqrt{7}} \]
Solution:
\[ x = \frac{2}{3 + \sqrt{7}} \times \frac{3 – \sqrt{7}}{3 – \sqrt{7}} = \frac{2(3 – \sqrt{7})}{9 – 7} \]
\[ = 3 – \sqrt{7} \]
\[ x – 3 = (3 – \sqrt{7}) – 3 = -\sqrt{7} \]
\[ (x – 3)^2 = (-\sqrt{7})^2 = 7 \]
\[ \therefore \text{Correct Answer: } 7 \ (\text{Option d}) \]