2. Relation and Function — MATHS STD 11 Science — Question

We have, $\left[x^2\right]=x+1$

Clearly, Eq.$(i)$ $\Rightarrow x$ is an integer $\quad \ldots (ii)$

$x^2-\left\{x^2\right\} =x+1$

$\Rightarrow \quad x^2-x-1 =\left\{x^2\right\}$

$Eq.(iii) \Rightarrow x^2-x-1 < 1$

$\Rightarrow \quad-1 < x < 2 \quad \ldots$ (iv)

From Eqs.$(ii)$ and $(iv)$ $\Rightarrow$ possible values of $x$ are $0$ and $1 .$

But $0$ and $1$ do not satisfy Eq.$(i)$.

$\therefore$ Equation $\left[x^2\right]=x+1$ has no soltuion.