The sum of two numbers is 17 and the sum of their square is 229. Find the numbers.

Question

Hello, can someone help me solve this problem because I’ve tried using | a² + (17a)^{2 = 229 | and I still don’t get it.}

Thank you

Answer 1

x+y + 17

x^2 + y^2 = 229

y=17-x

x^2 + (17-x)^2 = 229

x^2 + 289-34x + x^2 = 229

2x^2 -34x + 60 = 0

x^2 -17x +30 = 0

(x-15)(x-2) = 0

x = 2, 15

y= 17-2 or 17-15 = 15 or 2

the numbers are 2 and 15

you were close, but use 17-a not 17a