Q1 of 186 Page 4

The sum of the two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

Let the two numbers be x and y.

According to the question,


x + y = 18 …(i)


…(ii)


Eq. (ii) can be re - written as


…(iii)


On putting the value of x + y = 18 in Eq. (iii), we get



⇒ xy = 72



On putting the value of in Eq. (i), we get



⇒ 72 + y2 = 18y


⇒ y2 – 18y + 72 = 0


⇒ y2 – 12y – 6y + 72 = 0


⇒ y(y – 12) – 6(y – 12) = 0


⇒ (y – 6)(y – 12) = 0


⇒ y = 6 and 12




Hence, the two numbers are 6 and 12.


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