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Keep things simple:mark2142 said:
$$(x^2)^{1/2} = \sqrt{x^2} = |x|$$$$x^{(2*\frac 1 2)} = x$$
Is it Possible for x^2 to Exceed 900?
- Thread starter mark2142
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- Inequalities Precalculus
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Homework Help Overview
The discussion revolves around the inequality \(x^2 > 900\) and explores the implications of this condition in terms of the variable \(x\). Participants are examining the mathematical reasoning behind inequalities and the interpretation of square roots in this context.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants discuss the implications of the inequality \(x^2 > a\) and the correct interpretation of the resulting conditions for \(x\). There are questions about the ambiguity of expressions like \(x > \pm \sqrt{a}\) and the necessity of handling cases separately. Some participants suggest using absolute values to clarify the conditions.
Discussion Status
The discussion is active, with participants providing insights and questioning assumptions about the inequality and its implications. There is an ongoing exploration of how to correctly interpret and solve the inequality, with some guidance offered regarding the use of absolute values and the necessity of considering different cases.
Contextual Notes
Participants are navigating the complexities of inequalities and the conventions of square roots, particularly the distinction between principal square roots and the implications for negative values. There is a recognition of common misconceptions regarding the interpretation of square roots in the context of inequalities.
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