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Question
The sum of the square of 2 consecutive odd positive integers is 290.Find them.
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Solution
Let the numbers be X and X+ 2. Then as per question,
X2 + (X+ 2)2= 290
⇒ 2x2 + 4X - 286 = 0
⇒ X2 + 2X - 143 = 0
⇒ X2 + 13X - 11X -143 = 0
⇒ X (X +13)-11(X +13) = 0
⇒ (X+13 )(X-11) = 0. X can't be negative number as its natural number.
Hence, X = 11and X+ 2= 13.
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