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Solve 9x-2)[x]={x}-1, (where [x]a n d{x}...

Solve `9x-2)[x]={x}-1,` (where `[x]a n d{x}` denote the greatest integer function less than or equal to `x` and the fractional part function, respectively).

Text Solution

Verified by Experts

The correct Answer is:
`[1,2)`
For `x ge 2`, LHS is always non-negative and RHS is always negative.
Hence, for `x ge 2`, there is no solution.
If `1 le x lt 2, " then " (x-2)=(x-1)-1=x-2,` which is an identity.
For `0 le x lt 1,` LHS is 0 and RHS is (-)ve.
So, there is no solution.
Hence, `x in [1,2).`
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