(x^2+4)^2-11(x^2+4)+24=0

Jasonbradley

2 min read

·

Jun 17, 2024

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Solving the Equation (x^2 + 4)^2 - 11(x^2 + 4) + 24 = 0

This equation might look intimidating at first, but we can solve it using a simple substitution.

1. Substitution

Let's substitute y = x^2 + 4. This transforms our equation into:

y^2 - 11y + 24 = 0

2. Solving the Quadratic Equation

This is now a standard quadratic equation. We can solve it by factoring:

(y - 8)(y - 3) = 0

This gives us two possible solutions for y:

• y = 8
• y = 3

3. Back Substitution

Now, we need to substitute back x^2 + 4 for y in both solutions:

• x^2 + 4 = 8
• x^2 + 4 = 3

4. Solving for x

Solving for x in each equation:

• x^2 = 4 => x = ±2
• x^2 = -1 => x = ±i (where i is the imaginary unit, √-1)

Therefore, the solutions to the equation (x^2 + 4)^2 - 11(x^2 + 4) + 24 = 0 are:

• x = 2
• x = -2
• x = i
• x = -i