(Solution) - Consider the variation functions 1 bg and -(2025 Original AI-Free Solution)

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Consider the variation functions (1 = (( + bg and (2 = ( + cg, where f and g in (1 are the same functions as ( and g in (2, and a, b, and c are parameters whose values are chosen to minimize the variational integral W. Explain why (1 and (2 will give the same result for W when applied to the same problem.