Question

Let [ ] represents the greatest integer function and $[x^3+x^2+1+x]=[x^3+x^2+1]+x.$ The number of solution(s) of the equation in $\left|\right[x\left]\right|=2-\left|\right[x\left]\right|$ is

• A. $1$
• B. $Zero$
• C. $3$
• D. $2$

Answer 1

Answer: (D)

$2$

Given that,

$\left[x^3+x^2+1+x\right]=\left[x^3+x^2+1\right]+x$

Possible when $x^3+x^2+1$ and $x$ are in sequence .

no. of solution of the equation.

$\begin{array}{c}\left|\left[x\right]\right|=2-\left|\left[x\right]\right|\\ 2\left|\left[x\right]\right|=2\\ \left|\left[x\right]\right|=1\\ \left[x\right]=\pm 1\\ \left[x\right]=1\left[x\right]=-1\end{array}$

Therefore,

Number of solution $=2$

Hence, this is the answer.