SOLUTION: The difference between two positive numbers is 3 and the product between these two numbers is 28. Set-up two equations and solve to find the two numbers.

Question 389894: The difference between two positive numbers is 3 and the product between these two numbers is 28. Set-up two
equations and solve to find the two numbers.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
The difference between two positive numbers is 3
Let x and (x+3) represent the two positive numbers
Question states***
x(x+3) = 28
x^2 + 3x - 28 = 0
factoring
(x -7)(x-4)= 0
(x +7= 0
x = -7 Tossing out negative solution
(x-4)= 0
x = 4 the two positive numbers are 4 and 7 (4+3)
CHECKING Our Answer
4*7 = 28
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let a numbers be and , and let
The difference between them is

..........(1)
and the product between these two numbers is
...........(2)
solve the system:
..........(1)..solve for and substitute in (2)
...........(2)
---------------------------------
..........(1)
...........(2)

......solve for

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=3, and c=-28

Square 3 to get 9

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

since your numbers are positive, you will take only
to find
...plug in

so, your numbers are : and

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