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Here's a problem from one of the last (or previous of last) year, which bothers me ssssssoooooooo much. I've been working on this like a day or so, and haven't progressed very far. So, I'd be very glad if someone can give me a push on this.

[tex]\left\{ \begin{array}{ccc} e ^ x - e ^ y & = & \ln(1 + x) - \ln(1 + y) \\ y - x & = & a \end{array} \right.[/tex]

Prove that if a > 0, then the system of equation above has only one set of solution (x, y).

Thanks a lot.

[tex]\left\{ \begin{array}{ccc} e ^ x - e ^ y & = & \ln(1 + x) - \ln(1 + y) \\ y - x & = & a \end{array} \right.[/tex]

Prove that if a > 0, then the system of equation above has only one set of solution (x, y).

Thanks a lot.

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