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