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 = ³√46 x = -³√46 x = -√46 Solution to x² = 46 Solution to x³ = 46 Neither

Let’s evaluate each value of ( x ) against the equations ( x^2 = 46 ) and ( x^3 = 46 ).

1. ( x = sqrt{46} ):

– For ( x^2 = 46 ): ( (sqrt{46})^2 = 46 ) (True)

– For ( x^3 = 46 ): ( (sqrt{46})^3 ) is not equal to 46. (False)

– Solution: Solution to ( x^2 = 46 )

2. ( x = sqrt[3]{46} ):

– For ( x^2 = 46 ): ( (sqrt[3]{46})^2 = sqrt[3]{46^2} ) is not equal to 46. (False)

– For ( x^3 = 46 ): ( (sqrt[3]{46})^3 = 46 ) (True)

– Solution: Solution to ( x^3 = 46 )

3. ( x = -sqrt[3]{46} ):

– For ( x^2 = 46 ): ( (-sqrt[3]{46})^2 = (sqrt[3]{46})^2 ) is not equal to 46. (False)

– For ( x^3 =