Answer:
If x ≠ ±8, then x² ≠ 64.
Step-by-step explanation:
Given conditional statement:
[tex]\sf If \; x^2=64\;then\;x=\pm 8.[/tex]
The hypothesis of a conditional statement appears after the "if" part, and the conclusion of a conditional statement appears after the "then" part. Therefore, in this case:
- Hypothesis: x² = 64
- Conclusion: x = ±8
The contrapositive of a conditional statement is a new statement formed by both negating and reversing the order of the original hypothesis and conclusion. In other words, we switch the hypothesis and conclusion of the inverse statement.
In this case, we negate "x = ±8" to "x is not equal to ±8," and negate "x² = 64" to "x² is not equal to 64," then reverse the order. So, the contrapositive of the given statement is:
[tex]\Large\boxed{\sf If\; x \neq \pm8, \;then \;x^2 \neq 64.}[/tex]
