[QUOTE=grgrsanjay;552428]
i.e{2.635}=635
I think that's wrong.
{x}=x-[x]
the number of real values for x such that{ } where { } is the fractional part of x
i.e{2.635}=0.635
i think the answer is 1 cuz we get the answer right when we substitute 0 and i cannot think any other values that satisfy this equation
options are:
(A)0
(B)1
(C)4
(D)6
If is the fractional part of x then it must lie between 0 and 1, and therefore so must x.
Next, . If the fractional part of this is then the remaining part must be an integer. So we want to find numbers x between 0 and 1 that satisfy the equation for some integer n. The solution to the quadratic equation is (neglecting the negative square root because that leads to a negative value for x). That gives these solutions:
When n = 6 we get x = 1, which is too large. So there are six solutions in all.
I think if you simply plot and for , you will find there are 6 roots (i.e., intersections of the graphs of the two functions).
Maybe someone else will supply a more analytical approach-- but that's the "quick and dirty" way.
[edit] Beaten to the punch by Opalq, with a nicer solution![/edit]