Question

What is the solution set of the quadratic inequality x^2-5<_0

Answer 1

-sqrt(5) ≤ x ≤ sqrt(5)

Explanation:

x^2-5≤0

Add 5 to each side

x^2-5+5≤0+5

x^2 ≤5

Take the square root of each side, remembering to flip the inequality for the negative sign. Since this is less than we use and in between

sqrt(x^2) ≤ sqrt(5) and sqrt(x^2) ≥ -sqrt(5)

x ≤ sqrt(5) and x ≥- sqrt(5)

-sqrt(5) ≤ x ≤ sqrt(5)