 Hello and welcome to the session. Let us understand the following problem today. Find two consecutive positive integers, sum of whose squares is 365. Now let us write the solution. Let two consecutive positive integers be x and x plus 1. Given to us is, sum of the squares is equal to 365. Therefore the equation form will be x squared plus x plus 1 the whole square is equal to 365. Now solving this equation further we get x squared plus x squared plus 2x plus 1 is equal to 365 which implies 2x squared plus 2x plus 1 minus 365 is equal to 0 which implies 2x squared plus 2x minus 364 is equal to 0 which implies x squared plus x minus 182 is equal to 0. Now splitting the middle term we get x squared plus 14x minus 13x minus 182 is equal to 0 which implies taking x common from this we get x plus 14 and taking minus 13 common we get x plus 14 is equal to 0 which implies x minus 13 into x plus 14 is equal to 0. Therefore x minus 13 is equal to 0 and x plus 14 is equal to 0 which implies x is equal to 13 and x is equal to minus 14. x is equal to minus 14 not possible because we don't consider the negative values hence x is equal to 13. Therefore x plus 1 the other positive integer is equal to 13 plus 1 which is equal to 14 hence required positive integers are 13 comma 14. I hope you understood the problem bye and take care.