SOLUTION: Please help me solving it If {{{a=(1/2) (5-21^(1/2))}}} then the value of {{{a^3+a^(-3)-5a^2-5a^(-2)+a+a^(-1)}}}is?

Question 1046033: Please help me solving it
If then the value of is?
Answer by ikleyn(52898) (Show Source): You can put this solution on YOUR website!
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Please help me solving it
If then the value of is ?
~~~~~~~~~~~~~~~~~~~~~~~~~~

First, let us prove this statement: 


    if  a =   then   =  = .


Indeed,  * =  =  =  = 1.


OK. So, if  a = ,  then   =  =  = 5.


Having this, we can make the next step.

 +  =  =  = 23.   (I replaced here    by 5, based on the proof above )


Furthermore, 

 +  =           ( I applied the formula  = 

            =  = 110.             ( I replaced here  by 5  and replaced   +   by (23-1) = 22 based on results proved above).

Thus we have   = 5,   +  = 23  and   +  = 110.


Then the value under the question is  110 - 5*23 + 5 = 0.

For similar problems, see the lesson
- HOW TO evaluate expressions involving , and
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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