InterviewSolution
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InterviewSolution
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The number of integral solutions of the equation {x+1}+2x=4[x+1]-6 , is |
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Answer» Correct Answer - B We known that {x}=x-[x] `:. {x+1}+2x=4[x+1]-6` `implies x+1-[x+1]+2x=4[x+1]-6` `implies 3x+1 =4[x+1]-6` `implies 3x+1=5[x+1]-6` `implies 3x+1=5([x]+1)-6` ` implies 3x=5[x]-2 " "` (i) `implies 3([x]+{x})=5[x]-2` ` 3{x}=2[x]-2 " "`(ii) Now, `0 le {x} lt 1` `implies 0 le 3 {x} lt 3 ` `implies 0 le 2 [x]-2 lt 3 " "`[Using (ii)] `implies 2 le 2[x] lt 5 implies 1 [x] lt (5)/(2) implies 1 le [x] lt (5)/(2) implies [x]=1,2` From (i) , we have `[x]=-1implies x=1 and , [x]=2implies x=(8)/(3)` Hence, is x=1 the only integral solution of the given equation. |
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