SOLUTION: find three consecutive odd integers such that the sum of all three is 42 less than the product of the second and third integers.

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Question 531676: find three consecutive odd integers such that the sum of all three is 42 less than the product of the second and third integers.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Define the consecutive odd integers than:
x
x+2
x+4
.
3x+6 +42 = (x+2)(x+4)
.
3x + 48 = x^2 +6x + 8
.
x^2 +6x +8 = 3x +48
.
x^2 +6x +8 -3x -48 = 0
.
x^2 +3x -40 = 0
.
(x+8)(x-5) = 0
.
x = -8 or 5
.
Since -8 is not odd, we choose x = 5.
.
Answer: 5, 7, and 9.
.
Check the answer to determine if this is the correct answer.
Sum of all 3 = 21.
Product of 7*9 = 63.
63-21 = 42.
Correct.
.
Done.