The sum of the reciprocals of 2 consecutive integers is11/30 . Find the numbers

Question

It is an application problem have to find two numbers The sum of the reciprocals of  2 consecutive integers is 11/30. Find the numbers

Answer 1

1/a + 1/b = 11/30

 

(b+a)/ab = 11/30     Here you might see that a=5, b= 6 works. Or,

 

30(b+a) = 11ab

 

30(a+1 + a) = 11a(a+1)   by replacing b with a+1, which we could have done from the start

 

60a + 30 = 11a² + 11a

0 = 11a² - 49a - 30

 

(11a + 6)(a - 5) = 0

a = 5 or a = -6/11     by factoring or using the quadratic equation

 

The second value is not an integer.

 

So a,b = 5,6.