Step-by-step answer:
x^2-5<=0 .....................(1)
can be rewritten as
x^2<=5 ........................(2)
which gives the solution set
|x| <=sqrt(5) .........................(3)
(3) can be rewritten as
x<=sqrt(5), and -x <=sqrt(5) which gives a solution set of
x<=sqrt(5) and x>=-sqrt(5) .............(4)
The combined conditions of (4) can be rewritten as
-sqrt(5) <= x <= +sqrt(5)
which can also be rewritten in interval notation
[-sqrt(5), sqrt(5)]
The solution of the given inequality is (- √5) ≤ x ≤ (+√5).
"An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. "
The given inequality is:
x² - 5 ≤ 0
⇒ x² ≤ 5
⇒ x ≤ (± √5)
Therefore, the solution is (- √5) ≤ x ≤ (+√5).
Learn more about an inequality here:
https://brainly.com/question/1559622
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