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The sum of the squares of two consecutive odd positive integers is 394. Find them. |
Answer» Let’s assume the consecutive odd positive integer to be 2x – 1 and 2x + 1 respectively. [Keeping the common difference as 2] Now, it’s given that the sum of their squares is 394. Which means, (2x – 1)2 + (2x + 1)2 = 394 4x2 +1 – 4x + 4x2 +1 + 4x = 394 By cancelling out the equal and opposite terms, we get 8x2 + 2 = 394 8x2 = 392 x2 = 49 x = 7 and – 7 Since we need only consecutive odd positive integers, we only consider x = 7. Now, 2x – 1 = 14 -1 = 13 2x + 1 = 14 + 1 = 15 Thus, the two consecutive odd positive numbers are 13 and 15 respectively. |
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