"Let [x] denote the greatest integer less than or equal to x. Then, the values of x$\in$R satisfying the equation ${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$ lie in the interval :"

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"${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$

$\Rightarrow {[{e^x}]^2} + [{e^x}] + 1 - 3 = 0$

Let $[{e^x}] = t$

$\Rightarrow {t^2} + t - 2 = 0$

$\Rightarrow t = - 2,1$

$[{e^x}] = - 2$ (Not possible)

or $[{e^x}] = 1$ $\therefore$ $1 \le {e^x} < 2$

$\Rightarrow \ln (1) \le x < \ln (2)$

$\Rightarrow 0 \le x < \ln (2)$

$\Rightarrow x \in [0,\ln 2)$"

Let [x] denote the greatest integer less than or equal to x. Then, the values of x$\in$R satisfying the equation ${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$ lie in the interval :

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Let [x] denote the greatest integer less than or equal to x. Then, the values of x$\in$R satisfying the equation ${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$ lie in the interval :

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