# 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.