Determine whether each value of x in the table is a solution to the equation x² = 20, the equation x³ = 20, or neither.
Value of x
x = -√3/20
x = -√20
x = 3/√20
x = √20
Determine whether each value of x in the table is a solution to the equation x² = 20, the equation x³ = 20, or neither. Value of x x = -√3/20 x = -√20 x = 3/√20 x = √20
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Let’s evaluate each value of ( x ) against the equations ( x^2 = 20 ) and ( x^3 = 20 ).
1. ( x = -sqrt{3/20} )
– For ( x^2 = 20 ):
((- sqrt{3/20})^2 = frac{3}{20}), which is not equal to 20.
– For ( x^3 = 20 ):
((- sqrt{3/20})^3 = -frac{3sqrt{3}}{20sqrt{20}}), which is not equal to 20.
– Conclusion: Neither.
2. ( x = -sqrt{20} )
– For ( x^2 = 20 ):
((- sqrt{20})^2 = 20), which is correct.
– For ( x^3 = 20 ):
((- sqrt{20})^3 = -20sqrt{20}), which is not equal to 20.
– Conclusion: Solution to ( x^2 = 20 ) only.
3. ( x = 3/sqrt{20} )
– For ( x^2 = 20 ):
(left(frac{3}{sqrt