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for a real number x, let [x] denote...

for a real number x, let [x] denote the largest unteger less than or equal to x , and let {x} = x-[x] . The number of solution x to the equation [x] {x} =5 with `0 le xle 2015` is -

A

0

B

3

C

2008

D

2009

Text Solution

Verified by Experts

The correct Answer is:
D
`[x].{x} =5`
`{x} =(5)/([x])`
`therefore 0le (5) /([x]) lt 1`
`implies 1lt (5) /( {5})lt oo`
` implies 5lt [x]lt oo`
`So [x] =6,7,8*****2015`
`therefore x=[x]+{x} `
`{n+(5)/(n)|nin{6,7,.. .. .. 2015}}`
No of values of ''c' = 2009
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