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15 January, 06:43

Divide 29 into two parts so that the sun of the squares of the parts is 425. Find the value of each Part.

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Answers (2)
  1. 15 January, 07:10
    0
    The 2 parts are 13 and 16.

    Step-by-step explanation:

    WE can set up a system of equations. If the 2 parts are x and y we have:-

    x + y = 29

    x^2 + y^2 = 425

    From the first equation y = 29 - x, so substituting for y in the second equation:-:-

    x^2 + (29 - x) ^2 = 425

    x^2 + x^2 - 58x + 841 = 425

    2x^2 - 58x + 416 = 0

    2 (x^2 - 29x + 208) = 0

    We need 2 numbers whose sum is 29 and whose product is 208. Yhet are 13 and 16, so:-

    2 (x - 13) (x - 16) = 0

    x = 13, 16

    So y = 29-13, 29 - 16 = 16,13

    Thus one number is 13 and the other is 16.
  2. 15 January, 09:48
    0
    13 and 16

    Step-by-step explanation:

    let the 2 parts be x and y, then

    x + y = 29 → (1) and

    x² + y² = 425 → (2)

    From (1) → x = 29 - y → (3)

    substitute x = 29 - y into (2)

    (29 - y) ² + y² = 425 (expand factor)

    841 - 58y + y² + y² = 425 (rearrange into standard form)

    2y² - 58y + 416 = 0 ← in standard quadratic form

    divide all terms by 2

    y² - 29y + 208 = 0

    Consider the factors of 208 which sum to - 29

    These are - 13 and - 16, hence

    (y - 13) (y - 16) = 0

    equate each factor to zero and solve for y

    y - 13 = 0 ⇒ y = 13

    y - 16 = 0 ⇒ y = 16

    substitute these values into (3)

    x = 29 - 13 = 16 and x = 29 - 16 = 13

    The 2 parts are 13 and 16
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