The sum of two numbers is 6 and their product is 4. How do you find the larger of the two numbers?
2 Answers
Write the conditions as two equations and solve to obtain:
the larger of the two numbers is
Explanation:
Let the two numbers be
We are told that
[1]
and
[2]
Rearranging [1] we have
[3]
Substituting [3] into [2]
[4]
Which simplifies as
[5]
Using the quadratic formula
[6]
[7]
Since in [1] and [2]
The larger of these possibilities is
Write an equation and solve it.
The larger number is 5.236..
Explanation:
It is possible to do this using one variable.
If two numbers add up to 6, they can be written as
Their product is 4
This does not factorise, but it is a good example for using completing the square because
5.236 is the larger.