Applications of algebraic expressions

[MatinSAR]

Homework Statement

If $x+1/x=a$ and $x^{1394}+\frac {1}{x^{1394}}=b$ and $x^{1396}+\frac {1}{x^{1396}}=c$ then what is $x^{1398}+\frac {1}{x^{1398}}$ equal to?

Relevant Equations

Empty.

Hello. This is my answer:
https://up.maralhost.com/imagef-37f78ec7d1bd1-jpg.html
Can someone tell me If I am wrong?

Book's answer:

 

[MatinSAR]

My answer with more details :https://up.maralhost.com/imagef-37f78ec7d1bd1-jpg.html

 

[PeroK]

Homework Statement: If $x+1/x=a$ and $x^{1394}+\frac {1}{x^{1394}}=b$ and $x^{1396}+\frac {1}{x^{1396}}=c$ then what is $x^{1398}+\frac {1}{x^{1398}}$ equal to?
Relevant Equations: Empty.

Hello. This is my answer:
View attachment 330406
Can someone tell me If I am wrong?

Book's answer:
View attachment 330408

The book answer appears simple and unimpeachable to me.

 

[MatinSAR]

The book answer appears simple and unimpeachable to me.

Thanks for your reply.
You were not able to understand my answer(I am sorry it was not clear) or it was compeletly wrong?

More clear explanations and better quality:
https://up.maralhost.com/imagef-37f78ec7d1bd1-jpg.html

 

[PeroK]

Thanks for your reply.
You were not able to understand my answer(I am sorry it was not clear) or it was compeletly wrong?

More clear explanations and better quality:
https://up.maralhost.com/imagef-37f78ec7d1bd1-jpg.html

That looks like an alternative. $a,b,c$ are related, so there must be several different identities hidden there.

 

[MatinSAR]

That looks like an alternative. $a,b,c$ are related, so there must be several different identities hidden there.

Thank you again. For taking time to help me...
I will try to find a link between 2 answers. If it was successful I will inform...

 

[haruspex]

That looks like an alternative. $a,b,c$ are related, so there must be several different identities hidden there.

Yes, it is a poor question. E.g. you could solve the quadratic to find x as a function of a then plug that in.
It should be structured as "show that".