Question

Prove that for every real number x, x I- 0 if and only if x2 > O.

Answer 1

your question is unclear

Answer 2

\[\forall x \in x:x=0\iff x^2>0\]

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Answer 3

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Answer 4

Prove that for every real number x\[x \neq 0\] if and only if\[x ^{2}>0\]

Answer 5

\[(\rightarrow) x \neq0 \rightarrow x ^{2}>0\]
case:
\[1. x>0\]
\[x . x > 0 \]
\[x ^{2}>0\]

\[2. x<0 \Leftrightarrow -x>0\]
\[-x \times -x > 0 \]
\[x ^{2}>0\]

now, you just need to proof
\[(\leftarrow) x ^{2}>0 \rightarrow x\neq0\]