Problem 12 · Sum, product, sum of squares
The identity $(x+y)^2 = x^2 + y^2 + 2xy$ solves it without finding $x$ or $y$.
Integer answer, at most 4 digitsIf $x + y = 15$ and $xy = 19$, what is $x^2 + y^2$?
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: no need to solve the system: just expand the square of the sum.
$$x^2 + y^2 = (x+y)^2 - 2xy = 15^2 - 2 \cdot 19 = 225 - 38 = 187.$$
Answer: 187