Question

One positive number is 8 more than another. The sum of their squares is 104. Find both numbers.

Answer 1

let the two numbers be x and x+8

then x^2 + (x+8)^2 = 104

2x^2 + 16x + 64 = 104
x^2 + 8x - 20 = 0
(x+10)(x-2) = 0
x = -10 or x = 2

if x=2 then x=98 = 10

if x=-10 then x+8 = -2

so the two numbers are either 2 and 10
or -2 and -10