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

  • maths -

    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~ :)

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