CDS 2023 · PYQ · Algebra · medium
If 3^(x−1) + 3^(3−x) = 6, then what is 2^(x−1) + 2^(3−x) equal to?
Answer
The correct answer is C: 4. Let y = 3^(x−1), z = 3^(3−x). yz = 3² = 9 and y+z = 6, giving y = z = 3, so x−1 = 1, x = 2.
- A.3
- B.1
- C.4✓ Correct
- D.2
Let y = 3^(x−1), z = 3^(3−x). yz = 3² = 9 and y+z = 6, giving y = z = 3, so x−1 = 1, x = 2. Then 2^(x−1) + 2^(3−x) = 2 + 2 = 4.
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