1yes ans is R. plz help
find the largest interval in which x lies satisfying
x^{12}-x^{9}+x^{4}-x+1>0
-
UP 0 DOWN 0 0 4
4 Answers
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 Largest Interval for which $\mathbf{f(x)>0}$ is $\mathbf{x<1}$ }$\\\\ \boxed{\boxed{\mathbf{x\in\left(-\infty,1\right)}}}$
62arrey the answer is given by jagdish in #2...
he has proved it for both the cases... when x>1 and when x<1
so effectively he has proved it for all real values of x..