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Math Help - All reals numbers

  1. #1
    Super Member dhiab's Avatar
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    All reals numbers

    Find all reals numbers x , y : x + y = x y
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  2. #2
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    my attempt
    x+y=xy for real number
    (0,0),(2,2),(-1,1/2),(1/2,-1)


    Edit\\
    x+y=xy
    \Rightarrow \frac{1}{x}+\frac{1}{y}=1 \ which\  is\ a\ geometrical\ hyperbola

    \Rightarrow \frac{1}{y}=1 - \frac{1}{x} \quad or \quad \frac{1}{x}=1 - \frac{1}{y}
    \quad \Rightarrow \quad y=\frac{x}{x-1}\quad or \quad x=\frac{y}{y-1}
    therefore x \neq 1\ and\ y \neq 1 so,there are many solutions.
    Last edited by ramiee2010; October 19th 2009 at 11:25 PM. Reason: correction
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by ramiee2010 View Post
    my attempt
    x+y=xy for real number
    (0,0),(2,2),(-1,1/2),(1/2,-1)


    Edit\\
    x+y=xy
    \Rightarrow \frac{1}{x}+\frac{1}{y}=1 \ which\ is\ a\ geometrical\ hyperbola

    \Rightarrow \frac{1}{y}=1 - \frac{1}{x} \quad or \quad \frac{1}{x}=1 - \frac{1}{y}
    \quad \Rightarrow \quad y=\frac{x}{x-1}\quad or \quad x=\frac{y}{y-1}
    therefore x \neq 1\ and\ y \neq 1 so,there are many solutions.
    Hello THANK YOU
    I'can write the set of solutions is :

    S = \left\{ {} \right.\left( {x,\frac{x}{{x - 1}}} \right),\left( {\frac{x}{{x - 1}},x} \right)....\left. {x \in \Re ..\left( {x \ne 1} \right)} \right\}
    Last edited by dhiab; October 19th 2009 at 11:56 PM.
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