1/2x4-8x2=0

To solve the equation \( \frac{1}{2} x^4 - 8x^2 = 0 \), we can proceed as follows: 1. Factor the equation: First, let's factor out the common term. Notice that both terms contain \( x^2 \): \[ \frac{1}{2} x^4 - 8x^2 = 0 \implies x^2 \left( \frac{1}{2} x^2 - 8 \right) = 0 \] 2. Set each factor equal to zero: We have two factors: \[ x^2 = 0 \quad \text{or} \quad \frac{1}{2} x^2 - 8 = 0 \] **For the first factor:** \[ x^2 = 0 \implies x = 0 \] **For the second factor:** \[ \frac{1}{2} x^2 - 8 = 0 \implies \frac{1}{2} x^2 = 8 \implies x^2 = 16 \] So, \[ x = 4 \quad \text{or} \quad x = -4 \] 3. Combine the solutions: Thus, the solutions to the equation \( \frac{1}{2} x^4 - 8x^2 = 0 \) are: \[ x = 0, \quad x = 4, \quad x = -4 \]