A problem by Morgan Blake

Level pending

The polynomial \(f(x)\) is such that \[f(x^{2}+1) \equiv x^{4}+4x^{2}\] and \[f(x^{2}-1) \equiv ax^{4}+4bx^{2}+c\] What is the value of \(a^{2}+b^{2}+c^{2}\)?

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