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Find all real numbers x such that \(\left(\dfrac{x}{3}\right)^3-3x^2+81x-729=25+2(5)(3)+9.\)

 Aug 27, 2017
 #1
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(x/3)^3 -3x^2 + 81x - 729  =  25 + 2(5)(3) +  9

 

Simplify the right side and note that the left side can be factored as : 

 

(x/3 - 9)^3   =  64     take the cube root of both sides

 

(x/3 - 9)  = 4      add 9 to both sides

 

x/3  =  13       multiply both sides by 3

 

x  = 39   .....this is the only real solution......

 

 

 

cool cool cool

 Aug 27, 2017

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