%5E2%3D0.jpeg "(x^2+4)^2=0")
Solving the Equation (x^2 + 4)^2 = 0
This equation may seem a bit intimidating at first glance, but it's actually quite simple to solve. Let's break it down step by step:
Understanding the Equation
The equation (x² + 4)² = 0 represents a squared term being set equal to zero. This means that the expression inside the parentheses must also be equal to zero.
Solving for x
- Take the square root of both sides: √(x² + 4)² = √0
- Simplify: x² + 4 = 0
- Isolate x²: x² = -4
- Take the square root of both sides: x = ±√(-4)
- Simplify: x = ±2i (where 'i' is the imaginary unit, √-1)
The Solution
The solutions to the equation (x² + 4)² = 0 are x = 2i and x = -2i. These are complex numbers, as they involve the imaginary unit 'i'.
Key Takeaways
- Squaring an expression sets it to zero only if the expression itself is zero.
- The square root of a negative number results in an imaginary number.
This problem demonstrates the importance of understanding the properties of exponents and the concept of imaginary numbers when working with equations.