Which quadratic equation is equivalent to x^4 + 2x^2 + 6 = 0?

To solve the equation x⁴ + 2x² + 6 = 0, we can use substitution to transform it into a quadratic equation. Let’s set y = x². Therefore, x⁴ = (x²)² = y².

Substituting y into the original equation gives us:

y² + 2y + 6 = 0.

Now, we have a quadratic equation in terms of y. This equation can be solved using the quadratic formula, y = (-b ± √(b² – 4ac)) / 2a, where a = 1, b = 2, and c = 6.

The quadratic equation y² + 2y + 6 = 0 is equivalent to the original quartic equation. This means that we have successfully expressed the original equation as a quadratic equation in the variable y.