# SOLUTION: The sum of the squares of two cinsecutive positive odd numbers is 394. Find the numbers.

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 Click here to see ALL problems on Quadratic Equations Question 152204: The sum of the squares of two cinsecutive positive odd numbers is 394. Find the numbers. Answer by orca(409)   (Show Source): You can put this solution on YOUR website!Let x be the smaller odd number, then the greater one can be expressed in terms of x as x + 2. As the sum of the squares of two cinsecutive positive odd numbers is 394, we can setup an equation: x^2 + (x + 2)^2 = 394 Solving the quadratic equation for x, we have: x^2 + x^2 + 4x + 4 = 394 2x^2 + 4x + 4 = 394 2x^2 + 4x - 390 = 0 x^2 + 2x - 195 = 0 (x + 15)(x - 13) = 0 So x = -15 or x = 13 As x is positive number, we reject the solution x = -15. So the only solution is x = 13.