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shayhiddinovxasan93

09.07.2022

Mathematics

$x^3-6x^2+36x-216=x^2(x-6)+36(x-6)=(x-6)(x^2+36)=\\\\=(x-6)[x^2-36\cdot i^2)=(x-6)(x-6i)(x+6i)\\\\(x-6)(x-6i)(x+6i)=0\\\\\Leftrightarrow\ \ \ x-6=0\ \ \ \ or\ \ \ \ x-6i=0\ \ \ \ or\ \ \ \ x+6i=0\\\\.\ \ \ \ \ \ x=6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=6i\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-6i$

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