# Given #x+y=2# and #x^3+y^3=5#, what is #x^2+y^2#?

##### 2 Answers

It is

#### Explanation:

From

From

So we know that

and

If you add (1) and (2) you get

#### Explanation:

By applying the sum of cubes formula together with the given equations:

Now, by cubing the first given equation, we get

Substituting in our known values for

Substituting this back into