Question

divide 8 into two partssuch that the sum of their squares is 34

Answer 1

let x = first number
let 8-x = second number
then we set up the equation. It says that the sum of their squares must be 34. thus,
x^2 + (8-x)^2 = 34
then we solve for x:
x^2 + 64 - 16x + x^2 = 34
2x^2 - 16x + 64 = 34
2x^2 - 16x + 30 = 0
x^2 - 8x + 15 = 0
since it's factorable, we can just factor this, and not use the quadratic formula:
(x-3)(x-5) = 0
x = 3 (first number)
8-x = 5 (second number)

if you get the x = 5, you will obtain same set of answers since 8-5 = 3.

hope this helps~ :)