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avatar+263 

If 23=x^4+1/(x^4), then what is the value of x^2+1/(x^2)?

 

where do i even start? :'(

 Jan 26, 2020
 #1
avatar+26007 
+3

Sum of squares factorization:

 

A² + B² = (A+B)² − 2AB

 

A = x^2

B = 1/x^2

 

 

(x^2 + 1/x^2)^2 - 2 x^2(1/x^2)    =    (x^2 + 1/x^2)^2 -2    = 23

 (x^2 + 1/x^2)^2   = 25    

x^2+ 1/x^2   =  5     (taking the  positive root)

 Jan 26, 2020
 #2
avatar+263 
+1

ohh ok thank you!! i kept trying to square root things that i forgot about going the other way around haha

atlas9  Jan 26, 2020

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