Divided 29 into two parts so that the sum of the squares of the parts is 425 . Find the value of each part.​

Divided 29 into two parts so that the sum of the squares of the parts is 425 . Find the value of each part.​

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  1. Answer:

    Step-by-step explanation:

    Equations

    x + y = 29

    x^2 + y^2 = 425

    Solution

    y = 29 – x

    x^2 + (29 – x)^2 = 425

    x^2 + (841 – 58x + x^2 ) = 425

    x^2 – 58x + x^2 + 841 – 425 = 0

    2x^2 – 58x +416 = 0

    a = 2

    b = – 58

    c = 416

    You get two answers that look valid

    2x^2 – 58x + 416 = 0

    x^2 – 29x + 208 = 0           This factors

    (x – 16)(x – 13) = 0

    x = 16

    y = 13

    Now check it

    16^2 + 13^2 = ? 425

    256 + 169 =  425

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