SOLUTION: The product of second and third of 3 consecutive integers is 3 more than 3 times the second integer. find the 3 integers

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Question 534044: The product of second and third of 3 consecutive integers is 3 more than 3 times the second integer. find the 3 integers
Found 2 solutions by boilpoil, MathTherapy:
Answer by boilpoil(127) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the first integer
Then x+1 be the second
And x+2 be the third

%28x%2B1%29%28x%2B2%29=3%28x%2B1%29%2B3
x%5E2%2B2x%2Bx%2B2=3x%2B3%2B3
x%5E2%2B3x%2B2=3x%2B6
x%5E2%2B3x-3x=6-2
x%5E2=4
sqrt%28x%5E2%29=sqrt%284%29
x=+-2 ---Sorry can't enter the +_ Sign

So the first integer is either 2 or -2

The second integer
=+-2+1
=3/-1

The third integer
=+-3+1
=4/0

Filtering out:
3(4)=3(3)+3
12=9+3
12=12
TRUE

3(-1)=3(0)+3
-3=0+3
-3=3
FALSE

So the three integers are 3, 4 and 5

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
The product of second and third of 3 consecutive integers is 3 more than 3 times the second integer. find the 3 integers

Let the 1st integer be F

Then the other 2 are: F + 1, and F + 2

We have: (F + 1)(F + 2) = 3(F + 1) + 3

F%5E2+%2B+3F+%2B+2+=+3F+%2B+3+%2B+3

F%5E2+%2B+3F+-+3F+=+6+-+2

F%5E2+=+4

F, or 1st integer = ± 2

Therefore, the consecutive integers are either:highlight_green%282_3_and_4%29, or highlight_green%28-2_-1_and_0%29

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Check
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Integers are: 2, 3, & 4
Product of 2nd and 3rd: (3 * 4) = 3(3) + 3 ---- 12 = 9 + 3 ---- 12 = 12 (TRUE)

Integers are: - 2, - 1, & 0
Product of 2nd and 3rd: (- 1 * 0) = 3(- 1) + 3 ---- 0 = - 3 + 3 ---- 0 = 0 (TRUE)

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