The sum of two numbers is 20 and their squares is 272. Find the two numbers.

Question

The sum of two numbers is 20 and their squares is 272. Find the two numbers.

Answer 1

x + y = 20

x^2 + y^2 = 272

x= 20-y

(20-y)^2 + y^2 = 272

400-40y + y^2 + y^2 = 272

2y^2 -40y +128 = 0

y^2 - 20y + 64 = 0

(y-10)^2 = -64+100 = 36

y-10 = + or - 6

y = 4 or 16

the two numbers are 4 and 16