find three consecutive positive integers such that the product of the larger two is equal to twice the second integer plus twice the sum of all three integers

Question

find three consecutive positive integers such that the product of the larger two is equal to twice the second integer plus twice the sum of all three integers

Answer 1

s(s + 1) = 2s + 2(s - 1 + s + s + 1)

s² + s = 2s + 2s - 2 + 2s + 2s + 2

s² - 7s = 0

s(s - 7) = 0

s = 0

-1,0,1

Not all positive.

s - 7 = 0

s = 7

6,7,8