Question:
If \(y = 2 + \sqrt{5}\), find the value of \(y + 1/y\).
यदि \(y = 2 + \sqrt{5}\) है, तो \(y + 1/y\) का मान ज्ञात कीजिए।
Options:
- 3.47
- 4.47
- 5.44
- 6.5
- 3.47
- 4.47
- 5.44
- 6.5
Correct Answer: b)
Explanation:
\(y = \sqrt{5} + 2\).
\(\dfrac{1}{y} = \dfrac{1}{\sqrt{5} + 2} = \sqrt{5} – 2\).
\(y + \dfrac{1}{y} = (\sqrt{5} + 2) + (\sqrt{5} – 2) = 2\sqrt{5} \approx 2 \times 2.236 = 4.472 \approx 4.47\).
\(y = \sqrt{5} + 2\).
\(\dfrac{1}{y} = \sqrt{5} – 2\).
\(y + \dfrac{1}{y} = 2\sqrt{5} \approx 2 \times 2.236 = 4.47\)।