SOLUTION: if f(x^2 +1)=x^4+5x^2+3. what is f(x^2 -1)

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Question 1048295: if f(x^2 +1)=x^4+5x^2+3. what is f(x^2 -1)
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!

Let .
===> .
===> ,
do the rest...it will be good for you...
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
if f(x^2 +1)=x^4+5x^2+3. what is f(x^2 -1)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

My goal now is to present the polynomial in the right side,  ,  as a function (as a polynomial) of the argument  .  
We have

 =  +  =  +  -   = .


Thus   = .

      So, if I introduce new variable u = , then f(u) = .


Therefore,  =  =  = .

Answer.  If   = ,  then   =  = .


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