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Question Number 164451 by Zaynal last updated on 17/Jan/22

$$\mathbf{How}\mathbf{do}\mathbf{you}\mathbf{all}\mathbf{to}\mathbf{prove}\mathbf{is}\mathbf{true}\mathbf{or}\mathbf{false}??;$$$$$$$$\mathit{P}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{e}:$$$$\frac{1}{1+\mathbf{p}+{\mathbf{p}}^2+{\mathbf{p}}^3}+\frac{1}{1+\mathit{q}+{\mathit{q}}^2+{\mathit{q}}^3}+\frac{1}{1+\mathit{r}+{\mathit{r}}^2+{\mathit{r}}^3}+\frac{1}{1+\mathit{s}+{\mathit{s}}^2+{\mathit{s}}^3}⩾1$$

Commented by mr W last updated on 17/Jan/22

$$false!$$$$f\left(x\right)=\frac{1}{1+x+x^2+x^3}cangetanyvalues$$$$from-\mathrm{\infty }to+\mathrm{\infty }except0.therefore$$$$\frac{1}{1+\mathbf{p}+{\mathbf{p}}^2+{\mathbf{p}}^3}+\frac{1}{1+\mathit{q}+{\mathit{q}}^2+{\mathit{q}}^3}+\frac{1}{1+\mathit{r}+{\mathit{r}}^2+{\mathit{r}}^3}+\frac{1}{1+\mathit{s}+{\mathit{s}}^2+{\mathit{s}}^3}$$$$cangetanyvaluesfrom-\mathrm{\infty }to+\mathrm{\infty }.$$

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