Q39 of 40 Page 1

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.

Let the three consecutive positive integers be

(x – 1), xand (x + 1)


x2 + 1 – 2x + x2 + x = 46


2x2 – x – 45 = 0


2x2 – 10x + 9x – 45 = 0


2x(x – 5) + 9(x – 5) = 0


(x = 5)(2x + 9) = 0


x = 5,


Since, x are positive


∴ neglecting


∴ Integers


x – 1 = 5 – 1 = 4, x = 5


x + 1 = 5 + 1 = 6


∴ Required integers are 4, 5 and 6.


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