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solve-x-R-x-x-2-x-6-note-x-max-q-Z-q-x-




Question Number 146619 by mnjuly1970 last updated on 14/Jul/21
      solve ::   ( x ∈ R )                         [ x ] = [ x^( 2) − x −6 ]            note::   [x ] := max { q ∈ Z ∣ q ≤ x }
solve::(xR)[x]=[x2x6]note::[x]:=max{qZqx}
Answered by mindispower last updated on 18/Jul/21
[x]=n=[x^2 −x−6]  ⇒n<x<n+1,n≤x^2 −x−6<n+1  ⇒x^2 −x−6<x+1  ⇒x^2 −2x−7<0  ⇒x∈[1−2(√2),1+2(√2)]  if x∈[1−2(√2),−1[∪[−1,0[∪[0,1[∪[1,2[∪[2,1+2(√2)[  case one [x]=−2  ⇒−2≤x^2 −x−6<−1∩[−2,−1[  [x]=−1  −1≤x^2 −x−6<0  ∩[−1,0[  find 5 cases solve one by one
[x]=n=[x2x6]n<x<n+1,nx2x6<n+1x2x6<x+1x22x7<0x[122,1+22]ifx[122,1[[1,0[[0,1[[1,2[[2,1+22[caseone[x]=22x2x6<1[2,1[[x]=11x2x6<0[1,0[find5casessolveonebyone

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