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# Find all real numbers x such that ​

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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......

Aug 27, 2017