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If x3 _1/x3=14 then x_1/x=?

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If x3 _1/x3=14 then x_1/x=?

    • Posted by Nimrat Singla 8 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Soumya Ghoshal 8 years, 4 months ago

     

    {tex}​​​​​​​x^3-1/x^3=(x-1/x)^3+3×x×1/x(x-1/x){/tex}

       or,{tex}14= a^3+3a where x-1/x=a{/tex}

       or,{tex}a^3+3a-14=0{/tex}

    or,{tex}a³-2a²+2a²-4a+7a-14=0{/tex}

    or,{tex}a²(a-2)+2a(a-2)+7(a-2)=0{/tex}

    or,{tex}(a-2)(a²+2a+7)=0{/tex}

    Then,{tex}a=2{/tex}

    So,{tex} x-1/x=2{/tex}

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