Find all real numbers x such that \(\left(\dfrac{x}{3}\right)^3-3x^2+81x-729=25+2(5)(3)+9.\)
+80 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.
