Question bank/JEE Main/Mathematics

JEE MainMathematicsModerateFunctions

Sum of all real solution of equation
{x}+2x=[x]\{ x\} + 2x = \lbrack x\rbrack (where & are fractional part
function and greatest integer function respectively) is equal to

Show answer and solution
{x}+2{x}+2[x]=[x]\{ x\} + 2\{ x\} + 2\lbrack x\rbrack = \lbrack x\rbrack
3{x}=−[x]3\{ x\} = - \lbrack x\rbrack
[x]=0,−1,−2\lbrack x\rbrack = 0, - 1, - 2
{x}=13when{x}=−1\left\{ x \right\} = \frac{1}{3}when\{ x\} = - 1
{x}=23when[x]=−2\left\{ x \right\} = \frac{2}{3}when\lbrack x\rbrack = - 2

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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