SOLUTION: The sum of two numbers is 34 and their product is 168. Find the two numbers. I don't understand what product means. Thank you.

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Question 207364: The sum of two numbers is 34 and their product is 168. Find the two numbers. I don't understand what product means. Thank you.
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 34 and their product is 168. Find the two numbers. I don't understand what product means. Thank you.
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Product means multiplied. The product of 3 and 4 is 12, 3*4 = 12.
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x = 1 of the numbers
34-x is the other one.
x*(34-x) = 168
x^2 - 34x + 168 = 0
There are no integer solutions. Maybe a typo?
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-34x%2B169+=+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=%28-34%29%5E2-4%2A1%2A169=480.

Discriminant d=480 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--34%2B-sqrt%28+480+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-34%29%2Bsqrt%28+480+%29%29%2F2%5C1+=+27.9544511501033
x%5B2%5D+=+%28-%28-34%29-sqrt%28+480+%29%29%2F2%5C1+=+6.04554884989668

Quadratic expression 1x%5E2%2B-34x%2B169 can be factored:
1x%5E2%2B-34x%2B169+=+%28x-27.9544511501033%29%2A%28x-6.04554884989668%29
Again, the answer is: 27.9544511501033, 6.04554884989668. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-34%2Ax%2B169+%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of two numbers is 34 and their product is 168. Find the two numbers. I don't understand what product means. Thank you.

SUM means ADD, while PRODUCT means MULTIPLY

Let the first number = F, and the second number = S

Then since their sum is 34, we get: F + S = 34

Since their product is 168, then FS = 168

F + S = 34 -----> F = 34 - S -----> equation (i)

FS = 168 ------> equation (ii)

Substitute 34 - S for F in eq (ii) -----> S(34 - S) = 168
34S+-+S%5E2+=+168
S%5E2+-+34S+%2B+168+=+0

We're now looking for 2 factors whose products are + 168 (c * a), and whose sum is - 34. These 2 factors are (-28) and (-6).

Therefore, S%5E2+-+34S+%2B+168+=+0 -----> (S - 28)(S - 6) = 0

The smaller number is 6. Therefore, the two numbers are highlight_green%286%29 and highlight_green%2828%29