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

 Feb 6, 2019
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x^3/27 - 3x^2 + 81x -729 = 25+30+9

 

multiply everything by 27 to clear the fraction

 

x^3 - 81x^2+2187x - 19683 = 1728

 

subtract by 1728

 

x^3 - 81x^2 + 2187x - 21411=0

 

factoring yields:

 

x^3 - 8x^2 + 2187x -21411 = (x-39)(x^2-42x+549)

 

since two of the solutions are complex/imaginary numbers, the only solution is 39.

 Feb 6, 2019

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