SOLUTION: the difference of two numbers is 3 and the product is 10. what are the two numbers?

Question 490009: the difference of two numbers is 3 and the product is 10. what are the two numbers?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
let two numbers be and
the difference of two numbers is
.....1
and the product is
......2

to find out what are the two numbers, solve this system:

.....1
......2
--------------------------
.....1...solve for
......plug it in 2

......2

...use quadratic formula to solve for

....note that , , and

solutions:

or

now find

...plug in

or
...plug in

so, you have two sets of solutions, and they are:
1.

2.

check first set:

.....1

and the product is
......2

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
the difference of two numbers is 3 and the product is 10. what are the two numbers?

Let the first number be F, and the second S

We can therefore say that:

F - S = 3 ------ S = F - 3 ------ eq (i)
FS = 10 ------ eq (ii)

F(F - 3) = 10 ------ Substituting F - 3 for S in eq (ii)

(F - 5)(F + 2) = 0

F - 5 = 0, or F + 2 = 0

F, or first number = 5 or - 2

Substituting 5 for F in eq (ii), we find that S, or second number = 2
Substituting - 2 for F in eq (ii), we find that S, or second number = - 5

This means that the numbers are either: or

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