The sum of two numbers is 29 and the difference of their square is 145. Find their difference.

Question

The sum of the two numbers is 29 and the difference of their square is 145. Find their difference.

Answer 1

Let the number be a and b 

∴ According to the question,

   a + b = 29      ..........(1)

and a² - b² =145    ..........(2)

We know that,

also  a² - b² = ( a + b ) ( a - b)

⇒ 145 = 29 (a - b)

∴ a - b = 145 / 29 = 5

Hence, Their difference is 5