$\text{ If three successive terms of a G.P with common ratio }\mathrm{r}(\mathrm{r}>1),\text{form the sides }$$\text{ of a triangle }\mathrm{ABC}\text{ and }\left[\mathrm{r}\right]\text{ denotes greater integer function then }\left|\right[r]+[-r\left]\right|\text{ is }$

$a+ar>a{r}^2 \left(\sin ce sum of two sides of a triangle is greater than the third side\right)$

$\begin{array}{l}\to r^2-r-1<0\\ \frac{1-\sqrt{5}}{2}<\mathrm{r}<\frac{1+\sqrt{5}}{2}\\ \Rightarrow 1<\mathrm{r}<\frac{1+\sqrt{5}}{2}<2 \left(\mathrm{since} \mathrm{r}>1\right)\\ \Rightarrow \left[r\right]=1\\ \text{ Also }-\frac{(1+\sqrt{5})}{2}<-\mathrm{r}<-1\to [-r]=-2\\ \therefore \left|\right[r]+[-r\left]\right|==1\end{array}$