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Find all real values of X that satisfy the equation (x^2-82)^2=324. If you find more than one, then list the values separated by commas.

 Jan 25, 2019
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(x^2 - 82)^2 = 324

 

(x^2 - 82)^2 - 324 = 0      factor as a difference of squares

 

[ (x ^2 - 82 ) - 18  ]  [ (x^2 - 82) + 18] = 0

 

(x^2 - 100) (x^2  - 64)  =  0

 

(x + 10) (x - 10) (x - 8) (x + 8)  = 0        

 

Setting each factor to 0 and solving for x we have that

 

x = -10, 10, 8, -8

 

 

cool cool cool

 Jan 25, 2019
edited by CPhill  Jan 25, 2019

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