જો frac{1}{x^4+x^2+1}=frac{Ax+B}{x^2+x+1}+fra | vedclass

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(B) આપેલ છે,$\frac{1}{x^4+x^2+1} = \frac{Ax+B}{x^2+x+1} + \frac{Cx+D}{x^2-x+1}$.આપણે જાણીએ છીએ કે $x^4+x^2+1 = (x^2+x+1)(x^2-x+1)$.અંશને સરખાવતા:$1 =

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(B) આપેલ છે,$\frac{1}{x^4+x^2+1} = \frac{Ax+B}{x^2+x+1} + \frac{Cx+D}{x^2-x+1}$.આપણે જાણીએ છીએ કે $x^4+x^2+1 = (x^2+x+1)(x^2-x+1)$.અંશને સરખાવતા:$1 = (Ax+B)(x^2-x+1) + (Cx+D)(x^2+x+1)$સહગુણકોની સરખામણી કરતા:$A+C = 0, B-A+C+D = 0, A-B+C+D = 0, B+D = 1$.ઉકેલતા આપણને $A=\frac{1}{2}, B=\frac{1}{2}, C=-\frac{1}{2}, D=\frac{1}{2}$ મળે છે.તેથી,$A+B+C+D = 1$.તેથી,$\cos^{-1}(A+B+C+D) = \cos^{-1}(1) = 0$.

જો $\frac{1}{x^4+x^2+1}=\frac{Ax+B}{x^2+x+1}+\frac{Cx+D}{x^2-x+1}$ હોય,તો $\cos^{-1}(A+B+C+D)=$

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