InterviewSolution
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If a in R and the equation |
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Answer» <P>`(-1,0)UU(0,1)` Give, `a in R ` and EQUATION is `-3{x-[x]}^(2)+2{x-[x]}+a^(2)=0` Let `=x-[x],`then equation is `-3t^(2)+2t+a^(2)=0` `impliest=(a+-sqrt(1+3a^(2)))/(3)` `because t=x-[x]={X}""["fractional part"]` `because 0letle1` `0le(1+-sqrt(1+3a^(2)))/(3)le1` Taking positive SIGN, we GET `0le (1+sqrt(1+3a^(2)))/(3)lt1""p[because{x}gt0]` `impliessqrt(1+3a^(2))lt2impliesa+3a^(2)lt4` `impliesa^(2)-1lt0implies(a+1)(a-1)lt0` `therefore a in (-1,1)` for no integer solution of a, we consider `(-1,0)ii(0,1)` |
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