JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The value of \(3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\ldots \infty}}}}\) is equal to
- A \(1.5+\sqrt{3}\)
- B \(2+\sqrt{3}\)
- C \(3+2 \sqrt{3}\)
- D \(4+\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(1.5+\sqrt{3}\)
Step-by-step Solution
Detailed explanation
Let \(x=3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\ldots \infty}}}}\) So, \(x=3+\frac{1}{4+\frac{1}{x}}=3+\frac{1}{\frac{4 x+1}{x}}\) \(\Rightarrow(x-3)=\frac{x}{(4 x+1)}\) \(\Rightarrow(4 x+1)(x-3)=x\) \(\Rightarrow 4 x^{2}-12 x+x-3=x\) \(\Rightarrow 4 x^{2}-12 x-3=0\)…
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