The sum of both numbers is $3$

The sum of both numbers raised to the second power is $6.5$.

**Solution:**

How do we start?

First, we will represent both numbers with a single variable:

The first number: $X$

The second number: $3-X$

**How do we describe the second number?**

Let's say we had called it $Y$. We could have said, according to the problem's data: $x+y=3$, now let's solve for $Y$ we will get to the representation $Y=3-X$

Therefore, the second number is $3-X$

Next, we will make a quadratic equation based on the rest of the data from this problem.

We will square each of the numbers and add them, their sum must be $6.5$ according to what is stated in the problem.

$X^2+(3-x)^2=6.5$

$x^2+9-6x+x^2=6.5$

We will combine like terms, transpose members and obtain:

$2x^2-6x+2.5=0$

We will solve the equation based on the quadratic formula or the trinomial and it will give us:

$X=2.5 ,0.5$

**Observe:** These are not the two numbers we are looking for!

These are $2$ options for the first number represented with the $X$.

Now let's see what the two numbers are when the first one is $2.5$ then we will see what the two numbers are when the first one is $0.5$.

When the first number is $2.5$ and the second is $3-X$

The second number is: $0.5$,$3-2.5=0.5$

When the first number is $0.5$ and the second is $3-X$

The second number is: $2.5$,$3-0.5=2.5$