The sum of the squares of two consecutive odd integers is 1570. find the integers

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The sum of the squares of two consecutive odd integers is 1570. find the integers

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Adalynn 1 month 2021-08-14T18:05:46+00:00 2 Answers 0 views 0

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    0
    2021-08-14T18:06:51+00:00

    Answer:

    Step-by-step explanation:

    Let’s look at a few examples of two consecutive odd integers.

    1, 3

    11, 13

    55, 57

    Notice that the larger integer is always 2 more than the smaller one.

    If you let the smaller one be x, then the larger one is x + 2.

    Now we square the two numbers.

    The square of x is x^2.

    The square of x + 2 is (x + 2)^2.

    Now we add those two squares and set equal to 1570.

    x^2 + (x + 2)^2 = 1570

    x^2 + x^2 + 4x + 4 = 1570

    2x^2 + 4x + 4 = 1570

    2x^2 + 4x – 1566 = 0

    x^2 + 2x – 783 = 0

    783 is 290 * 27

    (x – 27)(x + 29) = 0

    x – 27 = 0 or x + 29 = 0

    x = 27 or x = -29

    Remember that x is the smaller of the two integers.

    If x = 27, then x + 2 is 29.

    If x = -29, then x + 2 is -27.

    The answer is:

    There are two pairs of integers

    One pair is 27 and 29.

    The other pair is -29 and -27.

    0
    2021-08-14T18:07:45+00:00

    Answer:

    (x)2+(x+2)2=1570

    now solve this equation and mark me a s brainliest

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