25
The sum of the squares of two consecutive odd numbers is 514. Find the numbers.
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Solution: Let two consecutive odd numbers be x and $x + 2$
A.T.Q.
$x^2 + (x + 2)^2 = 514$
$\Rightarrow 2x^2 + 4x - 510 = 0$ or $x^2 + 2x - 255 = 0$
$\Rightarrow (x + 17) (x - 15) = 0$
$\Rightarrow x = 15$
Required numbers are 15 and 17
A.T.Q.
$x^2 + (x + 2)^2 = 514$
$\Rightarrow 2x^2 + 4x - 510 = 0$ or $x^2 + 2x - 255 = 0$
$\Rightarrow (x + 17) (x - 15) = 0$
$\Rightarrow x = 15$
Required numbers are 15 and 17