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Properties of absolute inequality

For a real nu...

Question

For a real number x, let [x] denote the largest integer less than or equal to x, and let {x} = x - [x]. The number of solutions x to be equation [x]{x} = 5 with is 0 $\leq$ x $\leq$ 2015 is

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2008

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2009

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Solution

The correct option is D
2009

{x} = x - [x]

[x]{x} = 5 f $\neq$ 0

If = 5

0 $<$ f $<$ 1

Possible solutions

$(6 + \frac{5}{6}), (7 + \frac{5}{7}) . . . . . . ., (2014 + \frac{5}{2014}) = 2009$

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For a real number x, let [x] denote the largest integer less than or equal to x, and let {x} = x - [x]. The number of solutions x to be equation [x]{x} = 5 with is 0 ≤ x ≤ 2015 is

The correct option is D 2009 {x} = x - [x] [x]{x} = 5 f ≠ 0 If = 5 0 < f < 1 Possible solutions (6+56),(7+57).......,(2014+52014)=2009

For a real number x, let [x] denote the largest integer less than or equal to x, and let {x} = x - [x]. The number of solutions x to be equation [x]{x} = 5 with is 0 $\leq$ x $\leq$ 2015 is

The correct option is D
2009

{x} = x - [x]

[x]{x} = 5 f $\neq$ 0

If = 5

0 $<$ f $<$ 1

Possible solutions

$(6 + \frac{5}{6}), (7 + \frac{5}{7}) . . . . . . ., (2014 + \frac{5}{2014}) = 2009$