Given that P ( x ) = x 3 </msup> &#x2212;<!-- − --> 3 x . Prove that t

kincirrboh7

kincirrboh7

Answered question

2022-06-03

Given that P ( x ) = x 3 3 x. Prove that there exists a b c such that P ( a ) = b , P ( b ) = c , P ( c ) = a

Answer & Explanation

Angel Chan

Angel Chan

Beginner2022-06-04Added 6 answers

The roots of P(x)-x are 0,2,-2. but all of them are simple roots of P(P(P(x)))-x because
( P ( P ( P ( x ) ) ) x )
= P ( P ( P ( x ) ) ) P ( P ( x ) ) P ( x ) 1
= ( P ( x ) ) 3 1
= ( P ( 0 ) ) 3 1
= ( 3 ) 3 1
0
P ( P ( P ( x ) ) ) x has 27 roots while P ( x ) x has 3 roots, so the 24 numbers which are roots of the first but not second can be partitioned into 3-cycles under the action of P.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?