The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.

Explanation

Let the larger number be ` x ` and the smaller number be y.
Then, ` x + y = 1000" "` … (i)
and ` x^(2) - y ^(2)= 256000" " `… (ii)
On dividing (ii) by (i) , we get
` (x ^(2) - y ^(2))/( x + y ) = ( 256000)/( 1000) rArr x - y = 256 " "`...(iii)
Adding (i) and (iii), we get
` 2 x = 1256 rArr x = 628`
Substituting x = 628 in (i), we get `y = 372 `
Hence, the required numbers are 628 and 372