+0  
 
0
46
3
avatar+292 

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

 

 

 

-hihihi

 

😎😎😎

 Jan 11, 2021
 #1
avatar+114361 
+2

x^2  +  1/x^2        square both sides

 

(x^2  +  1/x^2)  ( x ^2   +  1/x^2)   =

 

x^4  +  x^2 (1/x^2)  + x^2(1/x^2)  +  1/x^4   =

 

x^4   +  1   +   1   +  1/x^4    

 

x^(4) + (1/x^4)   +  2   =   23  +  2   =   25

 

So

 

(x^2  + 1/x^)^2    =  25 

 

So

 

x^2/ + 1/x^2   =  5         (assuming x is real) 

 

 

cool cool cool

 Jan 11, 2021
 #2
avatar+292 
0

CPhill that is correct

 

 

-hihihi

 

😎😎😎

 Jan 11, 2021
 #3
avatar+112032 
0

hihi,

CPhill is a mathematician.

A more appropriate response would have been :

 

 

 

"Thanks very much CPhill.. 

 

I never would have thought of that by myself.  I hope next time I will be able to do a question like this by myself."

Melody  Jan 12, 2021

14 Online Users