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20 March, 20:42

Find the missing x - and y-values and Pythagorean triples can be generated using the identity given. Write the triple in parentheses, without spaces between the values, with a comma between values, and in order from least to greatest.

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  1. 20 March, 21:11
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    The complete question is:

    Find the missing x - and y-values and Pythagorean triples using the identity given:

    (x² - y²) ² + (2xy) ² = (x² + y²) ²

    X Value: 4

    Y Value: 3

    Pythagorean Triples:?

    X Value: 5

    Y Value:?

    Pythagorean Triples: (9,40,41)

    X Value:?

    Y Value: 3

    Pythagorean Triples: (27,36,45)

    X Value: 7

    Y Value: 5

    Pythagorean Triples:?

    Step-by-step explanation:

    Pythagorean triples are three numbers p, q, r, that satisfy Pythagoras' theorem.

    That is, they are numbers such that

    r² = p² + q².

    Given the identity

    (x² - y²) ² + (2xy) ² = (x² + y²) ²

    We can say tha

    p = x² - y²

    q = 2xy

    r = x² + y²

    Now, let us use this to solve the given problems.

    X Value: 4

    Y Value: 3

    p = 4² - 3² = 7

    q = 2*3*4 = 24

    r = 3² + 4² = 25

    Pythagorean Triples: (7,24,25)

    X Value: 5

    Y Value:? = (4)

    q = 2xy = 40

    2*5*y = 40

    y = 40/10 = 4

    Pythagorean Triples: (9,40,41)

    X Value:? = (6)

    Y Value: 3

    2xy = q = 36

    2*3*x = 36

    x = 36/6 = 6

    Pythagorean Triples: (27,36,45)

    X Value: 7

    Y Value: 5

    p = 7² - 5² = 24

    q = 2*7*5 = 70

    r = 7² + 5² = 74

    Pythagorean Triples:? = (24,70,74)
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