Question

find the smallest consecutive whole number such that the difference between one forth of the largest and one fifth of the smallest is at least three

Answer 1

let x, x+2, x+4 be three consecutive odd integers, then
:
2 * [(x+2) * (x+4)] = x * (x+2) + 91
:
2 * (x^2 +6x +8) = x^2 +2x +91
:
2x^2 +12x +16 = x^2 +2x +91
:
x^2 +10x -75 = 0
:
(x+15) * (x-5) = 0
:
x = -15 and x = 5
:
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there are two solutions
:
1) 5, 7, 9
:
2) -15, -17, -19
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