Solve `2[x]=x+{x},w h r e[]a n d{}` denote the greatest integer function and the fractional part function, respectively.

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

The total number of solutions of [x]^2=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively, is equal to: 2 (b) 4 (c) 6 (d) none of these

Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer function less than or equal to x and the fractional part function, respectively).

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

Solve : 4{x}= x+ [x] (where [*] denotes the greatest integer function and {*} denotes the fractional part function.

In the question, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. Solve: [x]^2-5[x]+6=0.

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. If y=3[x]+1=4[x-1]-10 , then find the value of [x+2y]dot

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tan)x sin x be an even function for all x in R Then the sum of all possible values of a (where [.] and {.} denot greatest integer function and fractional part function,respectively). (a) 17/6 (b) 53/6 (c) 31/6 (d) 35/3