COMEDK · Maths · 5. Sequences and Series
Let the HM and GM of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is
- A \(1: 2\)
- B \(2: 3\)
- C \(3: 4\)
- D \(1: 4\)
Answer & Solution
Correct Answer
(D) \(1: 4\)
Step-by-step Solution
Detailed explanation
H.M. \(=\frac{2 a b}{a+b} ; \mathrm{G} \cdot \mathrm{M} .=\sqrt{a b}\), Now, \(\quad \frac{\text { H.M. }}{\text { G.M. }}=\frac{2 \sqrt{a b}}{a+b}=\frac{4}{5}\) \(\Rightarrow \quad 25 a b=4(a+b)^{2}\) \(\Rightarrow \quad 4 a^{2}-17 a b+4 b^{2}=0\)…
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