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Question Number 204595 by SEKRET last updated on 22/Feb/24

$$\mathbf{f}\left(\mathbf{x}\right)={\mathbf{x}}^3-16{\mathbf{x}}^2-57\mathbf{x}+1$$$$\mathbf{f}\left(\mathbf{a}\right)=0\mathbf{f}\left(\mathbf{b}\right)=0\mathbf{f}\left(\mathbf{c}\right)=0$$$$\sqrt[5]{\mathbf{a}}+\sqrt[5]{\mathbf{b}}+\sqrt[5]{\mathbf{c}}=?$$

Answered by mr W last updated on 22/Feb/24

$$t=\sqrt[5]{x}\Rightarrow x=t^5$$$$t^{15}-16t^{10}-57t^5+1=0$$$$(t^3-t^2-2t+1)(t^{12}+t^{11}+...+2t+1)=0$$$$t^3-t^2-2t+1=0$$$$\Rightarrow \sqrt[5]{a}+\sqrt[5]{b}+\sqrt[5]{c}=t_1+t_2+t_3=1✓$$

Commented by SEKRET last updated on 22/Feb/24

$$\mathbf{thank}\mathbf{you}\mathbf{sir}$$

Commented by Satyam1234 last updated on 23/Feb/24

$$Howtogetthirdstepfromsecond?$$

Commented by mr W last updated on 23/Feb/24

$$factorizationofpolynomialwith$$$$helpofcomputerprogram$$

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