Question

What is the solution set of the quadratic inequality 4(x²) - 2 > 0?

Answer 1

To solve the quadratic inequality 4(x²) - 2 > 0, divide both sides by 4, move the constant term, take the square root, and simplify.

Step-by-step explanation:

To solve the quadratic inequality 4(x²) - 2 > 0, we need to find the solution set for x. Here are the steps:

1. Divide both sides of the inequality by 4 to simplify: (x²) - 1/2 > 0
2. Move the constant term to the other side of the inequality: (x²) > 1/2
3. Take the square root of both sides. Remember to consider both the positive and negative square roots: x > √(1/2) or x < -√(1/2)
4. Simplify the square root: x > (√2)/2 or x < - (√2)/2

So, the solution set of the quadratic inequality is x > (√2)/2 or x < - (√2)/2.