Question

The difference of two numbers is 5 and the difference between their squares is 65. Find the numbers.

Answer 1

Let the numbers be x and y, where x > y.
Then as per the question
x – y = 5                              …….(i)
`x^2 – y^2 = 65`                      …….(ii)
Dividing (ii) by (i), we get
`(x^2− y^2)/(x−y) = 65/5`
⇒ (𝑥−𝑦)(𝑥+𝑦)𝑥−𝑦 = 13
⇒ x + y = 13                    ……….(iii)
Now, adding (i) and (ii), we have
2x = 18 ⇒ x = 9
Substituting x = 9 in (iii), we have
9 + y = 13 ⇒ y = 4
Hence, the numbers are 9 and 4.