Question

If \[ \frac{x}{x^{4}+1}=\frac{Ax+B}{f(x)}+\frac{Cx+D}{g(x)}, \quad f(x)g(x)=x^{4}+1, \quad f(1)=2+\sqrt{2}, \] then \[ \frac{1}{D^{3}}+\frac{2}{B}= \]

• A. \(12\sqrt2\)
• B. \(16\sqrt2\)
• C. \(1\)
• D. \(0\) \bigskip

Hint:

For \(x^4+1\), always split into conjugate quadratics with \(\sqrt2 x\).

Answer 1

The Correct Option is B