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For c in IR, let $M_{c}=({x=(x_{1},x_{2},x_{3},x_{4}):|x|=1,x_{1}+x_{3}=c})$. Prove that $M_{c}$ is empty if |c|>square root of 2 and is a non- empty regular 2 surface if |c|< square root of 2. I'm guessing for the latter part I should use regular value theorem but I don't know where to start.

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