Discussion

Explanation:

Let the two no’s be a & b.

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

2aba+bab=1213

2abab=1213(a+b)

⇒ 13√ab = 6a + 6b

Dividing the whole equation by √ab, we get

⇒ 13 = 6ab+6ba

Substituting ab = 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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