Determine whether each value of x in the table is a solution to the equation x² = 46, the equation x³ = 46, or neither Value of x x = √46 x = -√46 x = -³√46 x = ³√46

Let’s evaluate each value of x against the equations x² = 46 and x³ = 46.

1. x = √46

– For x² = 46: (√46)² = 46, so this is a solution.

– For x³ = 46: (√46)³ = 46√46 ≠ 46, so this is not a solution.

2. x = -√46

– For x² = 46: (-√46)² = 46, so this is a solution.

– For x³ = 46: (-√46)³ = -46√46 ≠ 46, so this is not a solution.

3. x = -³√46

– For x² = 46: (-³√46)² = (³√46)² = ³√(46²). Since 46 is not the same as 46², this is not a solution.

– For x³ = 46: (-³√46)³ = -46, so this is not a solution.

4. x = ³√46

– For x² = 46: (³√46)² = ³√(46²), which is also not equal to 46, so this is not a solution.

– For x³ = 46: (³√46)³