Q4 of 39 Page 91

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)


Adding (i)&(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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