The sum of two numbers is 20, but the sum of their squares is 650. Find the numbers.

Question

The sum of two numbers is 20, but the sum of their squares is 650. Find the numbers.

Answer 1

x+y =20

x^2 + y^2 = 650

y = 20-x

x^2 + (20-x)^2 = 650

x^2 +400- 40x+x^2= 650

2x^2 -40x = -250

x^2- 20x + 125 = 0

(x-25)(x+5) =0

x= 25, -5

25^2 + (-5)^2 = 625+25 = 650

the two numbers are -5 and 25