Find the largest interval in which x lies satisfying
x^{12}-x^{9}+x^{4}-x+1>0
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1708$\textbf{Let $\mathbf{f(x) = x^{12}-x^9+x^4-x+1}$}\\\\ \textbf{Let $\mathbf{x\geq 1,}$ Then $\mathbf{f(x)=x^9(x^3-1)+x(x^3-1)+1>0}$ }\\\\ \textbf{Now for $\mathbf{x<1}$, Then $\mathbf{f(x)=x^{12}+x^4(1-x^5)+(1-x)}>0$ }\\\\ \textbf{So $\mathbf{f(x)>0\forall x\in \mathbb{R}}$ }