Question

1
The number of real solution(s) of the equation 3cos-lx =
x-[x]
where [:] represents the greatest integer function, is​

Answer 1

Given   :   3 Cos⁻¹x  = x  - [x]

To Find  :number of real solution

Solution:

3 Cos⁻¹x  = x  - [x]

Cos⁻¹x  =>   x ∈ [-1 , 1]

Cos⁻¹x  ∈  [0 , π]

=> 3 Cos⁻¹x  ∈  [0 , 3π]

 x  - [x]  ∈ [0 , 1)

x = 0  does not satisfy      

Hence there is only real solution

x ≈ 0.95025

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