Question Number 84293 by M±th+et£s last updated on 11/Mar/20
![solve in R x^([x]) +x^(2−[x]) =x^2 +1](https://www.tinkutara.com/question/Q84293.png)
$${solve}\:{in}\:{R} \\ $$$${x}^{\left[{x}\right]} +{x}^{\mathrm{2}−\left[{x}\right]} ={x}^{\mathrm{2}} +\mathrm{1} \\ $$
Answered by TANMAY PANACEA last updated on 12/Mar/20
$${when}\:\:\:\mathrm{1}>{x}\geqslant\mathrm{0} \\ $$$${L}={x}^{\mathrm{0}} +{x}^{\mathrm{2}−\mathrm{0}} =\mathrm{1}+{x}^{\mathrm{2}} ={R} \\ $$$${so}\:{x}\in\left[\mathrm{0},\mathrm{1}\right) \\ $$