5х^4-3^2-5=0

To solve the equation \( 5x^4 - 3^2 - 5 = 0 \), we can first simplify the equation. First, calculate \( 3^2 \): \[ 3^2 = 9 \] Now, substitute that back into the equation: \[ 5x^4 - 9 - 5 = 0 \] Combine like terms: \[ 5x^4 - 14 = 0 \] Now, add 14 to both sides of the equation: \[ 5x^4 = 14 \] Next, divide both sides by 5: \[ x^4 = \frac{14}{5} \] Now, take the fourth root of both sides: \[ x = \pm \sqrt[4]{\frac{14}{5}} \] This can also be simplified as: \[ x = \pm \frac{\sqrt[4]{14}}{\sqrt[4]{5}} \] So, the solutions to the equation \( 5x^4 - 3^2 - 5 = 0 \) are: \[ x = \frac{\sqrt[4]{14}}{\sqrt[4]{5}} \quad \text{and} \quad x = -\frac{\sqrt[4]{14}}{\sqrt[4]{5}} \]