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Thread: Sum of Two Integers

  1. #1
    Super Member harpazo's Avatar
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    Sum of Two Integers

    If the sum of the squares of two positive integers is 32 and their product is 9. What is the sum of two integers?

    x^2 + y^2 = 32
    xy = 9

    Is this the correct set up?
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  2. #2
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    Re: Sum of Two Integers

    Quote Originally Posted by harpazo View Post
    If the sum of the squares of two positive integers is 32 and their product is 9. What is the sum of two integers?

    x^2 + y^2 = 32
    xy = 9

    Is this the correct set up?
    Set up correct...but there is NO solution to the problem itself.

    Try sum of squares = 34 and product = 15
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  3. #3
    Super Member harpazo's Avatar
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    Re: Sum of Two Integers

    Very good.
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    Re: Sum of Two Integers

    Correct setup. Just apply (x+y)^2=x^2+y^2+2xy ans is 50^1/2.
    Last edited by mak29; Jan 5th 2019 at 11:56 AM.
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  5. #5
    Forum Admin topsquark's Avatar
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    Re: Sum of Two Integers

    Quote Originally Posted by mak29 View Post
    Correct setup. Just apply (x+y)^2=x^2+y^2+2xy ans is 50.
    Since $\displaystyle (x + y)^2 = 50$ then the sum $\displaystyle x + y = \pm \sqrt{50}$, which means at least one of x, y is not a positive integer.

    -Dan
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  6. #6
    Super Member harpazo's Avatar
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    Re: Sum of Two Integers

    Quote Originally Posted by mak29 View Post
    Correct setup. Just apply (x+y)^2=x^2+y^2+2xy ans is 50^1/2.
    Thanks.
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