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

Let the two numbers be x & Y


x + y = 18 (Given) …Equation 1


(Given) …Equation 2


Solving Equation 2 We get



Putting the value from Equation 1 we get


xy = 72


…Equation 3


Putting the value of Equation 3 in Equation 1 We get



x2 + 72 = 18x


x2 - 18x + 72 = 0


(x-6)2 = 0


x = 6


Putting the value of x in Equation 1 we get y = 12


The two numbers are 6 & 12


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