Solve equations I. a3 – 988 = 343 and II. b2 – 72 = 49 to determine a and b?
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Answer: B. If a ≥ b
Explanation
Solving the first equation yields a cubed root equal to twelve hundred thirty-one, resulting in a value of eleven for a. Solving the second equation results in b squared equaling one hundred twenty-one, which gives two possible values for b as positive or negative eleven. Comparing the calculated values shows that a is either strictly greater than or equal to b in all valid scenarios. Exponents and radicals are inverse mathematical operations used to scale numbers and solve polynomial equations of higher degrees. A quadratic equation involving squared terms always yields two roots that are equal in magnitude but opposite in sign. Inequality symbols such as greater than or equal to define the relative numerical order between two separate mathematical quantities.
Option A is incomplete because it ignores the scenario where b equals negative eleven, making them equal. Option C is entirely incorrect since a is never smaller than the possible values of b. Option D reverses the logical relationship by suggesting a is less than or equal to b.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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