Given \(\displaystyle{x}^{{{2}}}-{3}{x}+{6}={0}\) find \(\displaystyle{x}^{{{4}}}\) in terms

peggyleuwpodg

peggyleuwpodg

Answered question

2022-03-25

Given x23x+6=0 find x4 in terms of x.

Answer & Explanation

Abdullah Avery

Abdullah Avery

Beginner2022-03-26Added 19 answers

Step 1
you can start from here
x2=3x6
then multiply by x
x3=3x26x
now put x2=3x6 it means
x3=3(3x+6)6x=9x+186x
now you have x3 in terms of x.
zalutaloj9a0f

zalutaloj9a0f

Beginner2022-03-27Added 17 answers

Step 1
Your task is to find an equation of the form
x4=f(x)
where f has the least possible degree, given the relation
x23x+6=0.
Well, we can rearrange this to
x2=3x6,
then square both sides to get
x4=(3x6)2=9x236x+36.
Substituting
x2=3x6
again into this gives the final answer as
9(3x6)36x+36=9x18.

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