Question

The number of non-zero solutions of the equation x + 5{x} = 2[x] (where [x] denotes the greatest integer less than or equal to x and {x} denotes the fractional part of x) is

Answer 1

Answer:

(x−2)(x−{x})={x}−1⇒x  

2

−2x+1=(x−1){x}

⇒x=1 or x−1={x}⇒x=1 or[x]=1

⇒x∈[1,2)which satisfies given equation so infinitely many values