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Question
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
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Solution
Let the numbers be x-1, x, x+l . Then as per question,
(x-1)2 + (x) (x+l ) = 154
⇒ x2 -2x + 1+ x2 +x =154
⇒ 2 x2 - x - 153 = 0
⇒ 2 x2 - 18x +17x - 153 = 0
⇒ 2x (x-9) + 17 (x-9) = 0
⇒ (2x+17) (x-9) = 0
⇒ As the number have to be natural number, x=9
Hence, the numbers are 8,9 ,10 .
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