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Firstly, (x+y) squared is x2 + 2xy + y2 so if that is to equal x2 + y2 it follows that 2xy is zero, so either x=0 or y=0 or both are 0. It's also possible to read the question as x2 + y = x2 + y2 so then y=y2 so y= 0 or 1 in that case, with x being anything you like.

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Q: Describe the graph of the equation square of x plus y equals the square of x plus the square of y?
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