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8th Class Mathematics Algebraic Expressions Question Bank Algebra

  • question_answer
    If \[{{2}^{2x-y}}=32\]and \[{{2}^{x+y}}=16\] then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=(a+b+c)({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca)\]is equal to

    A) 9                                 

    B) 10

    C) 11                               

    D) 13

    Correct Answer: B

    Solution :

    \[{{2}^{2x-y}}=32\]\[\Rightarrow \] \[3{{x}^{3}}+4{{x}^{2}}-x+3\] \[\Rightarrow \] \[{{t}^{6}}+3{{t}^{2}}+10\]                 ?.(1) Again, \[{{2}^{x+y}}=16\Rightarrow {{2}^{x+y}}={{2}^{4}}\] \[\Rightarrow \]  \[{{x}^{4}}+2{{x}^{2}}-3x+7\]                     ?.(2) Adding (1) and (2), we get \[3x=9\] \[\Rightarrow \] \[{{x}^{3}}+{{x}^{2}}-4x+8\] \[\Rightarrow \] \[x=3\] Substituting this value for x in equation (2), we get \[3+y=4\]\[-1\]\[y=1\] Now, \[{{x}^{2}}+{{y}^{2}}={{3}^{2}}+{{1}^{2}}=9+1=10\]


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