Answer:
{[tex]x| -\sqrt{5} <x <\sqrt{5}[/tex]}
Step-by-step explanation:
We must solve the following inequality
[tex]x^2- 5<0[/tex]
factor the expression
[tex](x-\sqrt{5})(x+\sqrt{5})<0[/tex]
Case 1
[tex](x-\sqrt{5}) < 0[/tex] → [tex]x < \sqrt{5}[/tex]
[tex](x+\sqrt{5}) >0[/tex] → [tex]x > -\sqrt{5}[/tex]
{[tex]x| -\sqrt{5} <x <\sqrt{5}[/tex]}
Case 2
[tex](x-\sqrt{5}) > 0[/tex] → [tex]x > \sqrt{5}[/tex]
[tex](x+\sqrt{5}) <0[/tex] → [tex]x < -\sqrt{5}[/tex]
Without solution
The set solution is {[tex]x| -\sqrt{5} <x <\sqrt{5}[/tex]}
