Find the value of x if \(9^x - x^4 = 65\), given that x is a positive integer.
(a) 1
(b) 2
(c) 3
(d) 4

Answer: B. 2

• Answer: (b) 2
• Solution:
1. We can evaluate perfect powers to check for integer solutions by matching terms near 65.
2. Notice that the nearest perfect square above 65 is 81 (which is 9²).
3. Substituting x = 2 directly into the expression gives:
\(9^{2}-2^{4}=81-16=65\)
4. This perfectly satisfies the given equation, verifying that x = 2.

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