SOLUTION: I am thinking of three consecutive positive numbers. If I multiply the first with the third and then add the second, the result is 41. Let X be the smallest number. This is ho

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Question 102885: I am thinking of three consecutive positive numbers. If I multiply the first with the third and then add the second, the result is 41. Let X be the smallest number.
This is how far I have made, but I don't think I'm doing it right.
x
x+1
x+2
x+x+1+x+2=41
3x+3=41
3x+3-3=41-3
3x=38
x=38/3
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
This part of what you did is correct:
x
x+1
x+2
This is where you made a mistake:
x+x+1+x+2=41
The problem states:
If I multiply the first with the third and then add the second, the result is 41
So your equation should look like this:
x%28x%2B2%29%2B%28x%2B1%29=41
first multiply x across (x+2)
x%5E2%2B2x%2B%28x%2B1%29=41
next multiply 1 across (x+1)
x%5E2%2B2x%2Bx%2B1=41
now combine like terms
x%5E2%2B3x%2B1=41
now move 41 over by subtracting it from both sides
x%5E2%2B3x%2B1-41=41-41
x%5E2%2B3x-40=0
OK so now we have a quadratic equation in standard form. We can solve for x by factoring or by using the quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-40+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-40=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B3x%2B-40 can be factored:
1x%5E2%2B3x%2B-40+=+1%28x-5%29%2A%28x--8%29
Again, the answer is: 5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29

So the possible solutions for x are -8 and 5
However the problem states:
I am thinking of three consecutive positive numbers.
So we can throw out -8 as an extraneous solution.
Ok so the smallest number is 5
the next number is 5+1 which is 6
and the last number is 5+2 which is 7
Answer: The three consecutive positive numbers are 5, 6, and 7
Check by mulitiplying the first number by the third number and adding the second number. The result should be 41.
5 * 7 + 6 = 41
35 + 6 = 41
41 = 41