JEE Mains · Maths · STD 11 - 8. sequence and series
If the arithmetic mean of two numbers \(a\) and \(b, a>b>0\), is five times their geometric mean, then \(\frac{{a + b}}{{a - b}}\) is equal to
- A \(\frac{{\sqrt 6 }}{2}\)
- B \(\frac{3{\sqrt 2 }}{4}\)
- C \(\frac{{7\sqrt 3 }}{12}\)
- D \(\frac{{5\sqrt 6 }}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{{5\sqrt 6 }}{12}\)
Step-by-step Solution
Detailed explanation
\(A.T.Q.\), \(A.M.=5G.M.\) \(\frac{{a + b}}{2} = 5\sqrt {ab} \) \(\frac{{a + b}}{{\sqrt {ab} }} = 10\) \(\frac{a}{b} = \frac{{10 + \sqrt {96} }}{{10 - \sqrt {96} }} = \frac{{10 + 4\sqrt 6 }}{{10 - 4\sqrt 6 }}\) Use Componendo and Dividendo…
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