Discussion

Explanation:

Let the two no’s be a & b.

We know, G.M. = √ab and H.M. = 2ab/(a+b)

∴ $\frac{{\displaystyle \frac{2ab}{a+b}}}{\sqrt{ab}}=\frac{12}{13}$

⇒ $\frac{2ab}{\sqrt{ab}}=\frac{12}{13}(a+b)$

⇒ 13√ab = 6a + 6b

Dividing the whole equation by √ab, we get

⇒ 13 = $6\sqrt{\frac{a}{b}}+6\sqrt{\frac{b}{a}}$

Substituting $\sqrt{\frac{a}{b}}$ = x

⇒ 13 = 6x + 6/x

⇒ 6x² – 13x + 6 = 0

⇒ (3x - 2)(2x - 3) = 0

⇒ x = 2/3 or 3/2

∴ a/b = x² = 4/9 or 9/4.

Hence, option (a).

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