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Find two consecutive odd numbers, sum of whose squares is $650$.
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Let the consecutive odd numbers be $x$ and $x + 2 \implies x^2 + (x + 2)^2 = 650 \implies 2x^2 + 4x - 646 = 0$ or $x^2 + 2x - 323 = 0 \implies (x + 19)(x - 17) = 0 \implies x = 17 \therefore$ Odd numbers are $17, 19$