To determine which equations are true for x², we need to consider the basic properties and identities involving squares and the variable x.
1. **Equation 1**: x² = x * x
This equation is always true by the definition of squares. The square of any number (or variable) is equal to that number multiplied by itself.
2. **Equation 2**: x² ≥ 0
This is also true for any real number x. Since squaring a number (positive or negative) results in a non-negative value, x² will always be greater than or equal to zero.
3. **Equation 3**: x² + 1 = 0
This equation is false for real numbers because x², being non-negative, cannot equal -1 when you add 1, resulting in a negative value.
4. **Equation 4**: x² – 4 = 0
This equation can be true for specific values of x. Solving it gives x = 2 or x = -2.
In conclusion, when you check the equations, make sure to validate them based on their definitions and the properties of squares. Therefore, the true equations among the options will depend on the context provided. Always test for specific values of x when necessary!