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If $23=x^4+\frac{1}{x^4}$, then what is the value of $x^2+\frac{1}{x^2}$?

 Apr 28, 2020
 #1
avatar+738 
+2

Hi qwertyzz,

 

I'm really bad with these problems so this solution is probably wrong, but I'll give it a shot anyway!

 

If 23=x4+1x4 then what is the value of x2+1x2?

 

So how I did this is: 

 

First, I just set x2+1x2=y

 

If you square both sides of x2+1x2=y, you get (a2)2+2a21a2+(1a2)2=y2

 

So, this means that a4+1a4=y22.

 

We know that a4+1a4=23, so y22=23

 

So, we know y=±5

 

 

 

I hope this was right?

Please tell me if this is right!

:)

 Apr 29, 2020
edited by lokiisnotdead  Apr 29, 2020
edited by lokiisnotdead  Apr 29, 2020
edited by lokiisnotdead  Apr 29, 2020
 #2
avatar
+1

x4+1x4=23  (1)

x2+1x2 Square this 

(x2+1x2)2=x4+1x4+2 From (1) we know that x4+1x4=23 , substitute 

 

(x2+1x2)2=23+2=25

(x2+1x2)2=25 Square root both sides 

x2+1x2=+5 or 5

 Apr 29, 2020

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