# If the sum of the two numbers is 18 the sum of their reciprocals is 1/4 then what are the two numbers?

Let the 2 numbers be a & b

According to the question,

a + b = 18 ...... (i)

also,

ab = 72

Using (a – b)2 = a2 + b2 – 2ab

(a – b)2 = (a + b)2 – 4ab

(a – b)2 = 182 – 4×72

(a – b)2 = 324 – 288

(a – b)2 = 36

a – b = ±6 ...... (ii)

when a – b = 6;

2a = 24

a = 12 & b = 6

when a – b = – 6;

2a = 12

a = 6 & b = 6

So, the two numbers are 6 & 6.

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