Question

What is the solution set of the quadratic inequality x^2-5< or equal to 0​

Answer 1

`x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle`

Answer 2

For this case we must indicate the solution of the following inequality:

`x ^ 2-5 \leq0`

Adding 5 to both sides of the inequality:

`x ^ 2\leq5`

We apply square root on both sides of the inequality to eliminate the exponent:

`x \leq\pm \sqrt {5}`

So, we have two solutions:

`x\leq \sqrt {5}`

Since it is an inequality, the sign for the negative portion is changed:

`x\geq- \sqrt {5}`

Answer:

`x\leq \sqrt {5}\\x\geq-\sqrt {5}`