# If the sum of two numbers is #4# and their product is #3#, then what is the sum of their squares?

##### 3 Answers

#### Explanation:

The two numbers are

#x^2-4x+3 = (x-1)(x-3)#

In general we find:

#(x-a)(x-b) = x^2-(a+b)x+ab#

Notice that the coefficient of the middle term is

Given that the two numbers are

#1^2+3^2 = 1+9 = 10#

10

#### Explanation:

First, let's call the two numbers

We can then write:

We can solve the first equation for

Next, we can substitute

Solution 1)

Solution 2)

Substituting these back into the solution to the first equation gives:

Solution 1)

Solution 2)

The two numbers therefore are

The sum of their squares is therefore:

#### Explanation:

Calling the two numbers

#{ (x+y=4), (xy=3) :}#

and we find:

#x^2+y^2 = x^2+2xy+y^2-2xy#

#color(white)(x^2+y^2) = (x+y)^2-2xy#

#color(white)(x^2+y^2) = 4^2-2(3)#

#color(white)(x^2+y^2) = 16-6#

#color(white)(x^2+y^2) = 10#