Question: Total number of positive real values of x satisfying 2[x] = x + {x}, where [.] and {.} denote the gr...

Question

Total number of positive real values of x satisfying 2[x] = x + {x}, where [.] and {.} denote the greatest integer function and fractional part respectively, is equal to

Answer 1

Solution

2[x] = x + {x} ⇒ 2[x] = [x] + 2{x}

⇒ M = ⇒ 0 << 1 ⇒ 0 < [x] < 2

⇒ [x] = 0, 1

for [x] = 0, we get [x] = 0 r ⇒ x = 0

For [x] = 1, we get {x} = $\frac { 1 } { 2 }$ ⇒ x = $\frac { 3 } { 2 }$