SOLUTION: Find three consecutive integers such that four times the sum of all three is 2 times the product of the larger two.

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Question 377641: Find three consecutive integers such that four times the sum of all three is 2 times the product of the larger two.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Let x, (x+1) and (x+2) represent the three consecutive integers

Write as we Read***

4[x + (x+1) + (x+2)]=2(x+1)(x+2)

solving for s

4x + 4x + 4 + 4x + 8 = 2[x^2 + 3x + 2]

12x + 12 = 2x^2 + 6x + 4

2x^2 -6x - 8 = 0

x^2 - 3x  -4 = 0

(x-4)(x+1) = 0

(x-4)=0  x = 4 three consecutive integers are 4,5,6

(x+1)=0  x = -1 three consecutive integers are -1,0,1

CHECKING our Answers***

4 * 15 = 2*30 = 60

4 * 0 = 2 * 0*1 = 0