Fuctional Equation with some inequality












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QUESTION )
{2f(x₁)+4f(x₂)+....+2nf(xₙ)-nf(xₘ)} is divided by {f(xᵥ)} the quotient obtained was a square of (n) giving a remaider {0}.



given that, {m=(n-1)} and { v=(n-2) } also the above is true only if { n>2 }



The following inequality is a modified form of a famous inequality given with respect to above fuctional equation,



{f(xᵢ)²+f(xⱼ)²+2f(xₖ)²} > {4f(xᵣ)f(xₜ)}



again given that,



{k = (i+j)}
{r = (i-1)}
{t = (j-2)} and {(i+j)< (n)}
so find the value of function of (x₃) .



I just cannot understand what the inequality means for. I have reached till proving f(m)= f(v) , but unable to solve any furthur.
Please instruct if I am going wrong or give me a simple hint if i am going right proving f(m)= f(v) ??










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    0












    $begingroup$


    QUESTION )
    {2f(x₁)+4f(x₂)+....+2nf(xₙ)-nf(xₘ)} is divided by {f(xᵥ)} the quotient obtained was a square of (n) giving a remaider {0}.



    given that, {m=(n-1)} and { v=(n-2) } also the above is true only if { n>2 }



    The following inequality is a modified form of a famous inequality given with respect to above fuctional equation,



    {f(xᵢ)²+f(xⱼ)²+2f(xₖ)²} > {4f(xᵣ)f(xₜ)}



    again given that,



    {k = (i+j)}
    {r = (i-1)}
    {t = (j-2)} and {(i+j)< (n)}
    so find the value of function of (x₃) .



    I just cannot understand what the inequality means for. I have reached till proving f(m)= f(v) , but unable to solve any furthur.
    Please instruct if I am going wrong or give me a simple hint if i am going right proving f(m)= f(v) ??










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      QUESTION )
      {2f(x₁)+4f(x₂)+....+2nf(xₙ)-nf(xₘ)} is divided by {f(xᵥ)} the quotient obtained was a square of (n) giving a remaider {0}.



      given that, {m=(n-1)} and { v=(n-2) } also the above is true only if { n>2 }



      The following inequality is a modified form of a famous inequality given with respect to above fuctional equation,



      {f(xᵢ)²+f(xⱼ)²+2f(xₖ)²} > {4f(xᵣ)f(xₜ)}



      again given that,



      {k = (i+j)}
      {r = (i-1)}
      {t = (j-2)} and {(i+j)< (n)}
      so find the value of function of (x₃) .



      I just cannot understand what the inequality means for. I have reached till proving f(m)= f(v) , but unable to solve any furthur.
      Please instruct if I am going wrong or give me a simple hint if i am going right proving f(m)= f(v) ??










      share|cite|improve this question









      $endgroup$




      QUESTION )
      {2f(x₁)+4f(x₂)+....+2nf(xₙ)-nf(xₘ)} is divided by {f(xᵥ)} the quotient obtained was a square of (n) giving a remaider {0}.



      given that, {m=(n-1)} and { v=(n-2) } also the above is true only if { n>2 }



      The following inequality is a modified form of a famous inequality given with respect to above fuctional equation,



      {f(xᵢ)²+f(xⱼ)²+2f(xₖ)²} > {4f(xᵣ)f(xₜ)}



      again given that,



      {k = (i+j)}
      {r = (i-1)}
      {t = (j-2)} and {(i+j)< (n)}
      so find the value of function of (x₃) .



      I just cannot understand what the inequality means for. I have reached till proving f(m)= f(v) , but unable to solve any furthur.
      Please instruct if I am going wrong or give me a simple hint if i am going right proving f(m)= f(v) ??







      functions






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      asked Jan 17 at 14:24









      D.Ne.JBP.2D.Ne.JBP.2

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