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If x^2 + x - 1 = 0, find the value of x^4 - 3x^2 + 3.

 Nov 22, 2019
 #1
avatar+978 
+1

The root of x^2+x-1=0 is (-1+sqrt5)/2, so plug it in and you get 2.

 Nov 22, 2019
 #2
avatar+105476 
+1

x^2 + x  -  1  =  0

 

Rearrange as  :

 

x^2  =  1 - x      (1)

 

And

 

x^4 - 3x^2 + 3   =  

 

(x^2)^2 - 3x^2 + 3     (2)

 

Sub (1)  into (2)     and we have that

 

(1 - x)^2 - 3 (1 - x) +3

 

x*2 - 2x + 1 - 3 + 3x + 3

 

x^2 + x  - 2 + 3

 

( x^2 + x - 1 )  - 1 + 3

 

( x^2 + x - 1 ) + 2

 

0  +  2   =

 

2

 

 

cool cool cool

 Nov 22, 2019
edited by CPhill  Nov 22, 2019

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