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Find two consecutive odd positive integers, sum of whose square is 290?1. 11, 132. 5, 73. 13, 154. 7, 9 |
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Answer» Correct Answer - Option 1 : 11, 13 Calculation: Let the numbers be x and (x + 2) respectively ⇒ x2 + (x + 2)2 = 290 ⇒ x2 + x2 + 4 + (2 × x × 2) = 290 ⇒ 2x2 + 4 + 4x = 290 ⇒ 2x2 + 4x = 290 – 4 ⇒ 2x2 + 4x = 286 ⇒ x2 + 2x – 143 = 0 ⇒ x2 + 13x – 11x – 143 = 0 ⇒ x(x + 13) – 11(x + 13) = 0 ⇒ (x – 11) (x + 13) = 0 ⇒ x = 11, -13 The number can't be negative so value of x is 11 Second number = 11 + 2 = 13 ∴ The consecutive odd integers are 11 and 13 |
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