Find two consecutive positive numbers such that sum of their squares is 164?

Answer 1

Let the two consecutive positive numbers be ( x ) and ( x + 1 ). The equation for the sum of their squares is ( x^2 + (x + 1)^2 = 164 ). Simplifying this gives ( x^2 + x^2 + 2x + 1 = 164 ), or ( 2x^2 + 2x - 163 = 0 ). Solving this quadratic equation, we find ( x = 9 ) and ( x + 1 = 10 ). Thus, the two consecutive positive numbers are 9 and 10.