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
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
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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