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1. Q: If x^3 = 2x + 1
Show that: x^4 = x + 2x^2 and x^5 = 2 + 4x + x^2

Anyone know where to start with x^5 (done x^4 - obviously)?
2. (Original post by suejiaiuo)
Q: If x^3 = 2x + 1
Show that: x^4 = x + 2x^2 and x^5 = 2 + 4x + x^2

Anyone know where to start with x^5 (done x^4 - obviously)?
Very similar to x^4 but with a twist - ask yourself why there is no x^3 term in the answer for x^5, and where it could have 'disappeared' to.
3. (Original post by SeanFM)
Very similar to x^4 but with a twist - ask yourself why there is no x^3 term in the answer for x^5, and where it could have 'disappeared' to.
Are you supposed to multiply x4 = 2x2 + x by x to get x5 = 2x3 +x2? I tried various things but always get the same result.
I can't find how you get 2x3 to 2 + 4x
4. (Original post by suejiaiuo)
Are you supposed to multiply x4 = 2x2 + x by x to get x5 = 2x3 +x2? I tried various things but always get the same result.
I can't find how you get 2x3 to 2 + 4x
Correct

Like I said in my previous hint, the 'x^3' disappears from x^5 = 2x^3 + x^2... what if I said that it had been substituted out for something that you know from the question?
5. (Original post by SeanFM)
Correct

Like I said in my previous hint, the 'x^3' disappears from x^5 = 2x^3 + x^2... what if I said that it had been substituted out for something that you know from the question?
OOOOOOOOOOOOOOOOOOHHHHHHH
What a sneaky (insert swear word) question. Thanks for the help. Really really really appreciated it
Edit: So x5 = 2x3 + x2 ==> x5 = 2 ( 2x + 1 ) + x2 ==> x5 = 4x + 2 + x2

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