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

[zeion]

Homework Statement

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

Homework Equations

The Attempt at a Solution

$$-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}$$

But I can't square root a negative number?

 

[Mark44]

Homework Statement

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

Homework Equations

The Attempt at a Solution

$$-x^2 < 3 \Rightarrow x^2 > -3 \Rightarrow x > \sqrt{-3}$$

But I can't square root a negative number?

x² > -3 for all real numbers.

 

[zeion]

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.

 

[Mark44]

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.