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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If \[\mathbf{xy}\left( \mathbf{x}-\mathbf{y} \right)=\mathbf{1}\], then the value of \[\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{3}}}{{\mathbf{y}}^{\mathbf{3}}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{3}}}\]is:

    A)  0                                

    B)  1

    C)  3   

    D)  -3

    Correct Answer: C

    Solution :

    (c): \[xy\left( x-y \right)=1\Rightarrow x-y=\frac{1}{xy}\] Cubing both sides, \[{{x}^{3}}-{{y}^{3}}-3xy\left( x-y \right)=\frac{1}{{{x}^{3}}{{y}^{3}}}\] \[\Rightarrow {{x}^{3}}-{{y}^{3}}-3xy\times \frac{1}{xy}=\frac{1}{{{x}^{3}}{{y}^{3}}}\] \[\Rightarrow \frac{1}{{{x}^{3}}{{y}^{3}}}-{{x}^{3}}+{{y}^{3}}=3\]                              


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