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How to start this?

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)?
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.
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suejiaiuo
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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
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 :h:

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?
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suejiaiuo
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Original post by SeanFM
Correct :h:

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
(edited 7 years ago)

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