Question

Total number of solutions of ${\left[x\right]}^2=x+2\left[x\right]$, where $[.]$ and $\{.\}$ denotes the greatest integer function and fractional part respectively, is equal to

• A. $3$
• B. $4$
• C. $6$
• D. None of these

Answer 1

The correct option is A $3$

No. of solutions for $[x{]}^2=x+2[x]$

Let x be an integer

$x^2=x+2x$

$x^2=3x$

$x=3$ satisfies

So if $\left[x\right]=3$, then the equation satisfies.

So we have infinite solutions. [None- answer]

Note: If we want Integral values(integer value need to specify) In Question they haven't specified.