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Railways Quantitative Aptitude Power, Surds And Indices Sample Paper Surds Indices Sample Test Paper-4

  • question_answer
    If \[{{3}^{2x}}^{^{2}}-{{2.3}^{{{x}^{2}}+x+6}}+{{3}^{2(x+6)}}=0\] then the values of x are

    A)  \[x=-3,-2\]       

    B)  \[x=3,2\]

    C)  \[x=-3,2\]        

    D)  \[x=3,-2\]

    Correct Answer: D

    Solution :

    [d] Let \[{{3}^{x}}^{^{2}}=a\] and \[{{3}^{x+6}}=b\] the given equation reduces to \[{{a}^{2}}-2ab+{{b}^{2}}=0\] \[\Rightarrow \] \[{{(a-b)}^{2}}\] \[\Rightarrow \] \[a=b\] \[\therefore \] \[3{{x}^{2}}={{3}^{x+6}}\]                  \[[{{a}^{m}}={{a}^{n}}\,\,\,\,then\,\,\,\,m=n]\] \[\Rightarrow \] \[{{x}^{2}}=x+6\] \[\Rightarrow \] \[{{x}^{2}}-x-6=0\] \[\Rightarrow \] \[{{x}^{2}}-3x+2x-6=0\] \[\Rightarrow \] \[x(x-3)+2(x-3)=0\] \[\Rightarrow \] \[(x-3)(x+2)=0\] \[\Rightarrow \] \[x=3\,or\,x=-2\]


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