the product of two positive integers is 120 one number is 2 less than five times the other

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the product of two positive integers is 120 one number is 2 less than five times the other

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    2021-09-19T05:40:24+00:00

    x, y – two positive integers

    product of two positive integers is 120

    (1)    xy = 120

    one number is 2 less than five times the other

    (2)    x = 5y -2    substitute it to (1)

    (5y – 2)y = 120      use distributive property

    (5y)(y) – (2)(y) = 120

    5y² – 2y = 120      subtract 120 from both sides

    5y² – 2y – 120 = 0

    use quadratic formula

    a = 5, b = -2, c = -120

    b² – 4ac = (-2)^2 – 4(5)(-120) = 4 + 2400 = 2404

    √2404 is irrational number, therefore

    Answer: no solution in integer numbers

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