-[x]=3.solve for x .[ ] represents greatest integer function.

Hints: 1. x must be an integer 2. Monotonocity of f(x) = x³-x

solve graphically.

do you have access to graphers in JEE or AIEEE?

not a perfect method .but just a try.

we know,

x={x}+[x]

putiing [x] from above as x-{x}, we get the given eqn as,

{x}=3+x-x3

we know 0<={x} <1

so  0<= 3+x-x3<1

by obsevation we see that x must be lying between (1,2)

so [x]=1

so x=