Sum of squares of two natural numbers is 106. Square of smaller number is seven more than two times of bigger number. Find the numbers.

Question

Sum of squares of two natural numbers is 106. Square of smaller number is seven more than two times of bigger number. Find the numbers.

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Ximena 6 hours 2021-11-25T05:06:39+00:00 1 Answer 0 views 0

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    2021-11-25T05:08:12+00:00

    Answer:

    let the numbers be x and y

    x²+y²=106

    y² = 106-x²….(1)

    y² = 2x+7……(2)

    from (1) and (2)

    106- x² = 2x +7

    99 = 2x+x²

    x²+2x-99 =0

    x²+11x-9x-99 =0

    x(x+11) -9(x-+11) =0

    x-9=0 ; x= 9

    y²= 18+7

    y = 5

    therefore x= 9 and y= 5.

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