gif, fpf

find k such that 2x + {x} = k[x] has exactly 5 soutions where [.] is gif and {.} is fpf. i did get an ans but it didnt match with the ans key...and i was a bit confused too..can anyone explain how it is to be done
9 Replies
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@Apu
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CorrodedCoffin
CorrodedCoffin5mo ago
x=[x]+{x} using this in given eqn we get 3{x}=x {x} =x/3 0<= {x}<1 now consider 2 cases k-2>0 and k-2<0 and plugin {x} in terms of [x] in above inequality. now simply solve
Imine
ImineOP5mo ago
ohkk tho wont the no. of solution be infinite not 5 cuz fractional part varies with k
CorrodedCoffin
CorrodedCoffin5mo ago
It would imply that any value of k will give 5 values of [x] Ig u r not understanding the problem "has exactly 5 solutions" implies to [x] having 5 values In the certain condition we have obtained through manipulation
Imine
ImineOP5mo ago
oh but the way the question is framed, doesnt it imply x
CorrodedCoffin
CorrodedCoffin5mo ago
It does mean x but since we have eliminated x it becomes possible values of [x]
Imine
ImineOP5mo ago
+solved @hardcoreisdead
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