The sum of two numbers is 10.The sum of their squares is 52.Find the numbers.

Answer 1

one number --- x
the other ---- 10-x
x^2 + (10-x)^2 = 52
x^2 + 100 - 20x + x^2 = 52
2x^2 - 20x + 48 = 0
x^2 - 10x + 24 = 0
(x-6)(x-4) = 0
x = 6 or x=4

if one is 6, the other is 4
if one is 4 the other is 6
(symmetrical answers)

the two numbers are 6 and 4

check: 6+4 = 10
36+16 = 52
all is good!