The number of roots of `x^2-2=[sinx],w h e r e[dot]`stands for the gre – InterviewSolution

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1.	The number of roots of `x^2-2=[sinx],w h e r e[dot]`stands for the greatest integer function is0 (b)1 (c) 2(d) 3.
Answer» Correct Answer - C Given equation is `x^(2) -2=[sinx].` There are three possibilities: `[sinx]= -1, [sinx] =0,[sin x] =1` Case I: If `[sinx] = -1,` `x^(2)=1` or `x= +-1` When `x=1, [sin x]=0.` But ` x=-1 implies [sinx]= -1` `x= -1` is a solution. Case II: If `[sinx] =0,` the equation is `x^(2) =2` or ` x= +-sqrt(2)` `[sin sqrt(2)]=0` But ` [sin (-sqrt(2))]=-1.` So, `x=sqrt(2)` is a solution. Case III: If `[sinx] =1` `x=(pi)/(2),(5pi)/(2),(9pi)/(2)` Clearly, these values do not satisfy the original equation. Thus, number of solutions `=2`

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