Discussion

Explanation:

Given, a + b = 9 …(1)

and $\frac{1}{a}+\frac{1}{b}=\frac{1}{2}$ …(2)

⇒ $\frac{a+b}{ab}=\frac{1}{2}$

⇒ $\frac{9}{ab}=\frac{1}{2}$

⇒ ab = 18 …(3)

From (1) and (3), a(9 – a) = 18

⇒ a² – 9a + 18 = 0 

⇒ (a – 6)(a – 3) = 0

⇒ a = 6 or 3 

∴ When a = 6, b = 3 or when a = 3, b = 6.

Hence the numbers are 6, 3.

Hence, option (d).

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