Question

The solution set of inequation ${\log }_{1/3}(x^2+x+1)+1>0$ is

• A. $(-\infty ,-2)\cup (1,+\infty )$
• B. $[-1,2]$
• C. $(-2,1)$
• D. $(-\infty ,+\infty )$

Answer 1

The correct option is C $(-2,1)$

Given, ${\log }_{\frac{1}{3}}(x^2+x+1)+1>0$
$\Rightarrow {\log }_{\frac{1}{3}}(x^2+x+1)>-1$
$\Rightarrow x^2+x+1<{\frac{1}{3}}^{-1}$
$\Rightarrow x^2+x+1<3$
$\Rightarrow x^2+x-2<0$
$\Rightarrow (x-1)(x+2)<0$
$\Rightarrow x\in (-2,1)$
Hence, option 'C' is correct.