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Three consecutive natural numbers are such that the square of the middle numberexceeds the diference of the squares of the other two by 60. Find the numbers.15. |
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Answer» Since the middle number of the three consecutive numbers is x, the other two numbers are x -1 and x +1.According to the given condition, we havex² = [(x +1)² -(x -1)²] +60x² = (x² +2x +1) -(x² -2x +1) +60 = 4x +60x² -4x -60 = 0 => (x -10)(x +6) = 0x = 10 or -6Since x is a natural number, we get x = 10Hence the three numbers are 9, 10, 11 |
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