If the sum of the squares of nonnegative real numbers $a,b,$ and $c$ is $13$, and $ab + bc + ca = 6$, then what is the sum of $a,b,$ and $c$?
+96 So, we know that a^2 + b^2 + c^2 = 13.
Also, ab + bc + ca = 6.
And we want to find a + b + c. So, we sqaure a + b + c.
That would be a^2 + ab + ac + ba + b^2 + bc + ca + cb + c^2.
We group the squares together to get a^2 + b^2 + c^2, which is 13.
Then we group the ab or bc or ac together.
That gets us 2(ab + bc + ac) which is 2*6 which is 12.
Then we add to get 13 + 12 = 25.
