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8th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    If \[{{\left( \mathbf{x}+\mathbf{y} \right)}^{\mathbf{3}}}=\mathbf{1331}\] and\[{{\left( \mathbf{x}-\mathbf{y} \right)}^{\mathbf{5}}}=\mathbf{243}\], then find \[{{\mathbf{x}}^{\mathbf{2}}}-{{\mathbf{y}}^{\mathbf{2}}}.\]

    A)  33   

    B)  22                   

    C)  11                               

    D)  44

    Correct Answer: A

    Solution :

      (a) \[{{\left( x+y \right)}^{3}}=1331\,\,\,\,\,\,\Rightarrow x+y={{\left( 1331 \right)}^{\frac{1}{3}}}=11\] \[{{\left( x-y \right)}^{5}}=243\] \[\Rightarrow x-y={{\left( 243 \right)}^{\frac{1}{5}}}=3\Rightarrow \left( x+y \right)\left( x-y \right)=11\times 3=33.\]                   


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