Question

If $\left[x\right]$ denotes greatest integer function less than or equal to $x$ and $\left\{x\right\}$ denotes fractional part then the number of real values of $x$ satisfying equation $(x-2)\left[x\right]=\left\{x\right\}-1$, is

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

Answer: (D)

None of these

$(x-2)(x-\left\{x\right\})=\left\{x\right\}-1\Rightarrow x^2-2x+1=(x-1)\left\{x\right\}$
$\Rightarrow x=1orx-1=\left\{x\right\}\Rightarrow x=1or\left[x\right]=1$
$\Rightarrow x\in [1,2)$which satisfies given eqution so infinitely many values