Problem
ALG-B2-M10-P019 Power squeeze
Prove for every integer \(n>2\): \[(n-2)^{n+2}(n+2)^{n-2}
Hint 1. Compare the two extra factors \(n-2\) and \(n+2\).
Hint 2. Reduce the product to \((n^2-4)^n\).
Since \(n-2
A. Source analysis. Main objects: two bases around \(n\) with large exponents.
B. Insufficient first move. Direct logarithms or binomial expansion overcomplicate the problem.
C. Hidden observation. The extra exponents can be moved toward the larger base to obtain common exponent \(n\).
D. Required move. One must squeeze the expression through \((n^2-4)^n\).
E. Number of ideas. Two ideas: exponent balancing and base comparison.
F. Difficulty justification. Regional level 6: short solution, but the correct power comparison must be found.
G. Why it is not one-step. It is not one-step: first balance the exponents, then compare the resulting base.