JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The value of \(4+\frac{1}{5+\frac{1}{4+\frac{1}{5+\frac{1}{4+\ldots \ldots \infty}}}}\) is
- A \(2+\frac{2}{5} \sqrt{30}\)
- B \(2+\frac{4}{\sqrt{5}} \sqrt{30}\)
- C \(4+\frac{4}{\sqrt{5}} \sqrt{30}\)
- D \(5+\frac{2}{5} \sqrt{30}\)
Answer & Solution
Correct Answer
(A) \(2+\frac{2}{5} \sqrt{30}\)
Step-by-step Solution
Detailed explanation
\(y =4+\frac{1}{\left(5+\frac{1}{ y }\right)}\) \(y -4=\frac{ y }{(5 y +1)}\) \(5 y ^{2}-20 y -4=0\) \(y =\frac{20+\sqrt{480}}{10}\) \(y =\frac{20-\sqrt{480}}{10} \rightarrow\) rejected \(y =2+\sqrt{\frac{480}{100}}\)
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