If a = \(\frac{2 + \sqrt {3}}{2 - \sqrt {3}}\), b = \(\frac{2 - \sqrt {3}}{2 + \sqrt {3}}\), then
find (a + b)².
Answer & explanation
Correct answer: option 2
a = \(\frac{2 + \sqrt {3}}{2 - \sqrt {3}}\) × \(\frac{2 + \sqrt {3}}{2+ \sqrt {3}}\) = \(\frac{(2 + \sqrt {3})^2}{1}\) = 7 + 4\(\sqrt {3}\)
Similarly, b = 7 - 4\(\sqrt {3}\)
⇒ a + b = 7 + 4\(\sqrt {3}\) + 7 - 4\(\sqrt {3}\) = 14
⇒ (a + b)² = 196