Question

The number of real numbers that satisfy the relation $\left[x\right]=\frac{3}{2}\left\{x\right\}$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

We can write the given relation as {x} = $\frac{2}{3}$ [x]
We know 0 $\le$ {x} $\le$ 1. [x] takes only integer values.

So the values [x] can assume are 0 and 1. For any other value of [x],

.{x} = $\frac{2}{3}$ [x] goes out of its range([0, 1)).

When [x] = 0, {x} = 0

x = [x] + {x}

= 0 + 0 = 0

When [x] = 1, {x} = $\frac{2}{3}$
x = [x] + {x}
= 1 + $\frac{2}{3}$
= $\frac{5}{3}$
So the two values of x we got are 0 and $\frac{5}{3}$