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a x (a +1) = (a + 2)^2 - 28 ie a^2 + a = a^2 + 4a + 4 - 28 ie a^2 -a^2 + a - 4a = 4 - 28 ie -3a = -24 ie a = 8 Numbers are 8, 9 and 10. Check: 8 x 9 = 10^2 - 28 so 72 = 100 - 28 OK

Q: Find 3 consecutive number where the product of the smaller two numbers is 28 less than the square of the largest number?

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8,10,12

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the answer is 6

6 and 8. 6 * 8 = 48 6 * 6 = 36 48 - 36 = 12

Let the 3 consecutive number be represented by n, (n + 1) and (n + 2) Then, n(n + 1) + 37 = (n + 2)2 n2 + n + 37 = n2 + 4n + 4 3n = 33 n = 11 The three numbers are 11, 12 and 13.

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