Question:medium
If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:
If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:
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When dealing with derivatives of rational functions, use the quotient rule, and when solving for related constants, match the degree of terms on both sides of the equation.
Updated On: Nov 28, 2025
- \(P = x^2 - 2B, Q = 2x, R = 3x\)
- \(P = x^2 - 2Bx + C, Q = 4(x - B), R = 2\)
- \(P = 2x, Q = 2B, R = 2\)
- \(P = x, Q = x, R = 3\)
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