Determine whether each value of x in the table is a solution to the equation x² = 30, the equation x³ = 30, or neither.
Value of x
x = √30
x = 3√30
x = −√30
x = −3√30
Determine whether each value of x in the table is a solution to the equation x² = 30, the equation x³ = 30, or neither. Value of x x = √30 x = 3√30 x = −√30 x = −3√30
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Let’s evaluate each value of x to see if it solves either equation:
1. x = √30:
– For x² = 30: (√30)² = 30 (True)
– For x³ = 30: (√30)³ = 30√30 (False)
– Result: Solution of x² = 30.
2. x = 3√30:
– For x² = 30: (3√30)² = 9 * 30 = 270 (False)
– For x³ = 30: (3√30)³ = 27 * 30√30 = 810√30 (False)
– Result: Neither.
3. x = −√30:
– For x² = 30: (−√30)² = 30 (True)
– For x³ = 30: (−√30)³ = -30√30 (False)
– Result: Solution of x² = 30.
4. x = −3√30:
– For x² = 30: (−3√30)² = 9 * 30 = 270 (False)
– For x³ = 30: (−3√30)³ = -27 * 30√30 = -810√30 (False)
– Result: Neither.
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