Find all value of x where 5 - x^2 < 8

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Homework Help Overview

The problem involves solving the inequality 5 - x² < 8, which falls under the subject area of algebra and inequalities.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the manipulation of the inequality, noting that -x² < 3 leads to x² > -3. There is confusion regarding the implications of squaring negative numbers and whether this means x can take all real values.

Discussion Status

Some participants suggest that since x² > -3 is true for all real numbers, this might imply that the solution set includes all real numbers. However, there is no explicit consensus on this interpretation, and the discussion remains open to further exploration.

Contextual Notes

Participants are grappling with the implications of inequalities involving negative numbers and the properties of real numbers, particularly in relation to squaring.

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Homework Statement



Find all value of x where 5 - x^2 < 8

Homework Equations





The Attempt at a Solution



[tex]-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}[/tex]

But I can't square root a negative number?
 
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zeion said:

Homework Statement



Find all value of x where 5 - x^2 < 8

Homework Equations





The Attempt at a Solution



[tex]-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}[/tex]

But I can't square root a negative number?
x2 > -3 for all real numbers.
 
Mark44 said:
x2 > -3 for all real numbers.

So does that mean x is the set of all real numbers? Because any real number squared is positive.
 
Yes, the solution set is all real numbers. Something to remember: If you ever get an equation where x2 > some negative number, the inequality is true for all real numbers.
 

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