Question

The sum of the number and it's reciprocal is 61/30, find the numbers

Answer 1

Solution:-

Let the one number be 'x'

So, its reciprocal will be 1/x

Now, according to the question.

x + 1/x = 61/30

(x² + 1)/x = 61/30 after cross multiplying, we get

30x² + 30 = 61x

30x² - 61x + 30 = 0

30x² - 36x - 25x + 30 = 0

6x(5x - 6) - 5(5x - 6) = 0

(6x - 5) (5x - 6) = 0

6x = 5

x = 5/6

And,

5x = 6

x = 6/5

So, the numbers are 5/6 and 6/5

Answer.