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Maths-

General

Easy

Question

The total number of solutions of $left square bracket x right square bracket to the power of 2 end exponent equals x plus 2 open curly brackets x close curly brackets comma$ where [.] and {.} denote greatest integer function and fractional part, respectively is equal to

2
4
6
8

The correct answer is: 4

$0 £ open curly brackets x close curly brackets less than 1 p open square brackets x close square brackets stack I with hat on top fraction numerator 9 minus square root of 3 over denominator 2 end fraction comma 0 comma fraction numerator 1 plus square root of 3 over denominator 2 end fraction$ $therefore left square bracket x right square bracket equals negative 1 comma 0 comma 1 comma 2 comma left curly bracket x right curly bracket equals fraction numerator 2 over denominator 3 end fraction 0 comma 0 comma fraction numerator 2 over denominator 3 end fraction$
$therefore x equals negative fraction numerator 1 over denominator 3 end fraction comma 0 comma 1 comma fraction numerator 8 over denominator 3 end fraction$

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