Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

Question

Raindrop

Mathematics

18 March, 01:57

Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

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Cason · Answer 1

Assume the smaller one is x, then the other ones will be x+2 and x+4

x (x+2) + 2 = 5 (x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6) (x+3) = 0

-> x = 6 or - 3, since x must be positive, then x = 6

So the numbers are: 6, 8, 10