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
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
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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 =