Mathematics - Functions Question with Solution | TestHub

Given:

$x^2-4x+\left[x\right]+3=x\left[x\right]$

$\Rightarrow x^2-4x+3=x\left[x\right]-\left[x\right]$

$\Rightarrow \left(x-1\right)\left(x-3\right)=\left[x\right]\left(x-1\right)$

$\Rightarrow x=1$ or $x-3=\left[x\right]$

If $x-3=\left[x\right]$

$\Rightarrow x–\left[x\right]=3$

$\Rightarrow \left\{x\right\}=3$

which is not Possible, since $\left\{x\right\}\in [0,1)$.

Hence, $x=1$ is the only one solution in $\left(-\infty ,\infty \right)$.