Question

Решите уравнение
(х-2) ^3 - (х-3) ^3 = 27

Answer 1

$left(x-2right)^3-left(x-3right)^3=27medskip\left(x-2-x+3right)left(left(x-2right)^2+left(x-2right)left(x-3right)+left(x-3right)^2right)=27medskip\x^2-4x+4+x^2-5x+6+x^2-6x+9=27medskip\3x^2-15x+19=27medskip\3x^2-15x-8=0medskip\x_{1,2}=dfrac{15pmsqrt{225+96}}{6}=dfrac{15pmsqrt{321}}{6}medskip\left[begin{gathered}x=dfrac{15+sqrt{321}}{6}\x=dfrac{15-sqrt{321}}{6}end{gathered}$

Ответ. $x=dfrac{15+sqrt{321}}{6},;,x=dfrac{15-sqrt{321}}{6}$