Let the solution of the equation 5{x}=2[x]+x be a/4. Then the value of a is where {.} and [.] represents fractional part function and greatest integer function respectively.
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Solution
5{x}=2[x]+x ⇒5{x}=2[x]+[x]+{x} ⇒4{x}=3[x]...(1)
We know, 0≤{x}<1 ⇒0≤4{x}<4 ⇒0≤3[x]<4 ⇒0≤[x]<4/3
Now, for equation (1) 4{x}=3[x] ⇒4(x−[x])=3[x] ⇒4x−4[x]=3[x] ⇒x=7/4[x] ⇒x=0,7/4
Sum =0+7/4=7/4 ∴a4=74 ⇒a=7