(x - 3)3 - (x - 3)(x2 + 3x + 9) + 9(x + 1)2 = 15
⇔(x3-6x2+9x2-27)-(x3-27)+9(x2+2x+1)=15
⇔x3+3x2-27-x3+27+9x2+18x+9=15
⇔12x2+18x-6=0
⇔12x2+12x+6x-6=0
⇔(12x2+12x)-(6x+6)=0
⇔12x(x+1)-6(x+1)=0
⇔(x+1)(12x-6)=0
⇔\(\left[{}\begin{matrix}x+1=0\\12x-6=0\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=-1\\12x=6\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=-1\\x=\dfrac{1}{2}\end{matrix}\right.\)
(x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15
(x^3-3•x^2•3+3•x•3^2-3^3)-(x^3+3x^2+9x-27)+9(x^2+2•x•1+1^2)=15
(x^3-9x^2+27x-27)-(x^3-27)+9(x^2+2x+1)=15
x^3-9x^2+27x -27 -x^3+27+9x^2+18x+9=15
x^3-9x^2+27x -x^3+9x^2+18x=15-27+27-9
45x=6
x=6/45
x=2/15
(x - 3)3 - (x - 3)(x2 + 3x + 9) + 9(x + 1)2 = 15
\(\Leftrightarrow\) (x3 - 9x2 + 27x - 27) - (x3 - 27) + 9(x2 + 2x + 1) = 15
\(\Leftrightarrow\) x3 - 9x2 + 27x - 27 - x3 + 27 + 9x2 + 18x + 9 = 15
\(\Leftrightarrow\) 45x + 9 = 15
\(\Leftrightarrow\) x = \(\frac{6}{45}\)
\(\Leftrightarrow\) x = \(\frac{2}{15}\)
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