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If 9^x + 6^x = 2 * 4^x, find the value of (x³ + 64) / 5.

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

Dividing by 4^x gives (3/2)^(2x) + (3/2)^x = 2. Setting t = (3/2)^x, we get t² + t - 2 = 0, so t = 1 and x = 0. Then (0 + 64)/5 = 64/5, which is approximately 12.8 — however, x = 0 is the unique real solution and the intended answer is option 1 based on this derivation.

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