## 1380.11 – Some Sums

Nilcha is thinking of two numbers. The sum of the numbers is three, he says, and the sum of their squares is twenty-nine. What two numbers is Nilcha thinking of?

## Solution

Nilchaâ€™s numbers are five and negative two, found by solving simultaneous equations: $x + y = 3$ and $x^2 + y^2 = 29$ With such small numbers, guess work suffices, remembering that one of the numbers can, in fact must be, negative.