The sum of two integers is 9 and the sum of their squares is 41. Find the integers.

Answer 1

x+y = 9 y=9-x

x^2 +y^2 = 41

x^2 +(9-x)^2 = 41

x^2 +81 -18x +x^2 = 41

18x = 81-41 = 40

x = 40/18 = 20/9 = 2 2/9

y = 9-20/9 = 61/9 = 6 7/9

20/9 squared + 61/9 squared = 400/81 + 3721/81= 4121/81= 81(41)/81 = 41