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.

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) (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.
------------
Product means multiplied. The product of 3 and 4 is 12, 3*4 = 12.
----------------
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=480 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 27.9544511501033, 6.04554884989668. Here's your graph:

Answer by MathTherapy(10552) (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

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 - 28)(S - 6) = 0

The smaller number is 6. Therefore, the two numbers are and

RELATED QUESTIONS
The sum of two numbers is thirteen and their product is 21. Find the two... (answered by checkley79)
the sum of two numbers is 22 and their product is 120. Find the two... (answered by Fombitz,MathLover1)
The sum of two numbers is 33 and their product is 270. Find the two... (answered by Alan3354)
The sum of two numbers is 33 and their product is 270. Find the two... (answered by MathLover1)
The sum of two numbers is 20. Find the numbers and their product if their product is a... (answered by math_helper)
The sum of two numbers is 4 and their product is (- 32). Find the numbers. (answered by checkley77,rfer)
the sum of two numbers is 27 and their product is 152, find the... (answered by Alan3354,checkley77)
the sum of two numbers is 16 and their product is 48. find the numbers (answered by Alan3354)
the sum of two numbers is 11, and their product is 30. Find the... (answered by Fombitz,LinnW)