[tex]x\in\{-1,2,3,5\}[/tex]
[tex]\displaystyle x^4-9x^3+21x^2+x-30=0\Big.\\x^4-8x^3-x^3+15x^2+8x^2-2x^2-15x+16x-30=0\Big.\\x^4-8x^3+15x^2-x^3+8x^2-15x-2x^2+16x-30=0\Big.\\x^2(x^2-8x+15)-x(x^2-8x+15)-2(x^2-8x+15)=0\Big.\\(x^2-8x+15)(x^2-x-2)=0\Big.\\(x-5)(x-3)(x-2)(x+1)=0\Big.\\\left[\begin{array}{c}x=5\\x=3\\x=2\\x=-1\end{array}\right.[/tex]
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Ответ:
[tex]x\in\{-1,2,3,5\}[/tex]
Объяснение:
[tex]\displaystyle x^4-9x^3+21x^2+x-30=0\Big.\\x^4-8x^3-x^3+15x^2+8x^2-2x^2-15x+16x-30=0\Big.\\x^4-8x^3+15x^2-x^3+8x^2-15x-2x^2+16x-30=0\Big.\\x^2(x^2-8x+15)-x(x^2-8x+15)-2(x^2-8x+15)=0\Big.\\(x^2-8x+15)(x^2-x-2)=0\Big.\\(x-5)(x-3)(x-2)(x+1)=0\Big.\\\left[\begin{array}{c}x=5\\x=3\\x=2\\x=-1\end{array}\right.[/tex]