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