# The sum of two numbers is 15 and sum of their reciprocals is . Find the numbers.

Let the two numbers be x and y.

According to the question,

x + y = 15 …(i)

…(ii)

Eq. (ii) can be re - written as

…(iii)

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

xy = 50

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

50 + y2 = 15y

y2 – 15y + 50 = 0

y2 – 10y – 5y + 50 = 0

y(y – 10) – 5(y – 10) = 0

(y – 5)(y – 10) = 0

Hence, the two numbers are 5 and 10.

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