# An easy difficult problem

Every body knows that:

$$x_{1}^2+x_{2}^2........x_{n}^2 =0\Longrightarrow x_{1}=0\wedge x_{2}=0........\wedge x_{n}=0$$.

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??

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CompuChip
$$a + b = 0$$
$$a = x_1^2 + x_2^2 + \cdots + x_n^2, \quad b = x_{n + 1}^2$$
and use that $x_i^2 \ge 0$ for all i.