+0  
 
0
101
4
avatar+168 

If \(x=\frac{\sqrt5-3}{2}\)

 

Find \(x(x-1)(x-2)(x-3)\)

Rollingblade  Jun 4, 2018
 #1
avatar+907 
+2

Hey Rollingblade!

 

We have two equations we can manipulate here:

 

First, let's change the second one:

 

\(x(x-1)(x-2)(x-3)\\ =[x(x-3)][(x-1)(x-2)]\\ =(x^2-3x)(x^2-3x+3)\)

 

Now, we can change the first one:

 

\(x=\frac{\sqrt5-3}{2}\\ 2x+3=\sqrt5\\ (2x+3)^2=5\\ 4x^2+12x+4=0\\ x^2+3x=-1\)

 

We now found the value of \(x^2+3x\), and can plug this into the original equation. 

 

\((x^2-3x)(x^2-3x+3)=-1(-1+3)=\boxed{-2}\)

 

I hope this helped,

 

Gavin. 

GYanggg  Jun 4, 2018
 #2
avatar
+1

well that was a long answer, but sorry gavin, x^2-3x does not equal x^2+3x

 

you could just sub in [(sqrt5-3)/2] everywhere you see x then simplify

whether you change the equation like gave did, may or may not help

 

[(sqrt5-3)/2] * [(sqrt5-3)/2 - 2/2] * [(sqrt5-3)/2 - 4/2]  *  [(sqrt5-3)/2 - 6/2]

 

{[(sqrt5-3)/2] * [(sqrt5-5)/2]} * {[(sqrt5-7)/2]  *  [(sqrt5-9)/2]}

 

{[(-8sqrt5-10)/4]} * {[(-16sqrt5-58)/4]}

 

[(624sqrt5+1220)/16] 

 

or 99.17 rounded

Guest Jun 4, 2018
 #4
avatar+907 
0

Yeah, I have realized. 

 

I was so caught up in writing the solution to the problem, 

 

I just made a careless error. 

 

Thanks for spotting it. 

GYanggg  Jun 4, 2018
 #3
avatar+26841 
+2

Hmm.

 

Alan  Jun 4, 2018

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.