The total number of solutions of [x]2=x+2(x}, where [.] and {.} denote the greatest integer function and the fractional part function, respectively, is equal to
A
2
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B
3
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C
4
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D
6
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Solution
The correct option is C 4 (x]2=x+2(x}⇒(x]2=(x]+(x}+2(x}⇒(x]2=(x]+3(x}⇒(x}=(x]2−(x]3∵0≤(x}<1⇒0≤(x]2−(x]3<1⇒0≤(x]2−(x]<3⇒(x]2−(x]−3<0&(x]2−(x]>0⇒(x]∈(1−√132,0]∪[1,1+√132)⇒(x]=−1,0,1,2⇒(x}=23,0,0,23⇒x=−13,0,1,83