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Question Number 27975 by NECx last updated on 18/Jan/18

solve the inequality  (1/(x^2 +x+1))>0

$${solve}\:{the}\:{inequality} \\ $$ $$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}>\mathrm{0} \\ $$

Answered by mrW2 last updated on 18/Jan/18

(1/(x^2 +x+1))=(1/(x^2 +2×(1/2)x+((1/2))^2 +(3/4)))=(1/((x+(1/2))^2 +(3/4)))>0  ⇒−∞<x<+∞

$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}×\frac{\mathrm{1}}{\mathrm{2}}{x}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}}=\frac{\mathrm{1}}{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}}>\mathrm{0} \\ $$ $$\Rightarrow−\infty<{x}<+\infty \\ $$

Commented byRasheed.Sindhi last updated on 18/Jan/18

N̸i̸c̸e̸ S̸i̸r̸!̸

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