fambrini wrote:What is the value of a� - b�?
1) a² - b² = 16
2) a + b = 8
Alternate approach:
Statement 1:
If b=0, then a²=16, implying that a = ±4.
In this case, a� - b� = (±4)� - 0� = 4�.
If b=4, then a²=0, implying that a=0.
In this case, a� - b� = 0� - (±4)� = -(4�).
Since a� - b� can be different values, INSUFFICIENT.
Statement 2:
If b=0, then a=8.
In this case, a� - b� = 8� - 0� = 8�.
If b=8, then a=0.
In this case, a� - b� = 0� - 8� = -(8�).
Since a� - b� can be different values, INSUFFICIENT.
Statements combined:
Statement 1 can be rephrased as follows:
(a+b)(a-b) = 16.
Since a+b=8, a-b = 2.
Since we have two distinct linear equations and two variables, we can solve for both variables.
Thus, the value of a� - b� can be determined.
SUFFICIENT.
The correct answer is
C.
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