Let the numbers be ‘a’ and ‘b’
Given, sum of two numbers is 18. The sum of their reciprocals is 1/4
⇒ a + b = 18
⇒ b = 18 – a
Also, 1/a + 1/b = 1/4
⇒ 1/a + 1/(18 – a) = 1/4
⇒ 18 × 4 = 18a – a2
⇒ a2 – 18a + 72 = 0
⇒ a2 – 12a – 6a + 72 = 0
⇒ a(a – 12) – 6(a – 12) = 0
⇒ (a – 6)(a – 12) = 0
⇒ a = 6, 12
Numbers are are 6,12 or 12, 6
