Find two consecutive positive integers sum of whose squares is 365.

Explanation

Let two consecutive positive integers be `x and x+1`
`" " therefore x^(2) + (x+1)^(2) = 365`
`rArr x^(2) + x- 182=0`
`" " (x + 14) (x - 13)=0`
`" " therefore x = 13`
Hence two consecutive positive integers are 13 and 14