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[tex]x_{1}^2+x_{2}^2........x_{n}^2 =0\Longrightarrow x_{1}=0\wedge x_{2}=0........\wedge x_{n}=0[/tex].

But how do we prove that?

Perhaps by using induction?

For n=1 .o.k

Assume true for n=k

And here now is the difficult part .How do we prove the implication for n=k+1??