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Question Number 181779 by DAVONG last updated on 30/Nov/22

3^(4x−11) +3^(10−x^2 ) +3^((x−2)^2 ) =6x−x^2

34x−11+310−x2+3(x−2)2=6x−x2

Answered by manxsol last updated on 01/Dec/22

6x−x^2 ≫0⇒0≪x≪6 −x^2 +6x−t=0⇒△=6^2 −4t △≫0⇒t≪9 3^(4x−11) ≪3^1 ⇒x≪3 3^(10−x^2 ) ≪3^1 ⇒−3≪x∪x≫3 3^((x−2)^2 ≪) 3^(1⇒) 1≪x≪3 t≪9 solution x=3

6x−x2≫0⇒0≪x≪6−x2+6x−t=0⇒△=62−4t△≫0⇒t≪934x−11≪31⇒x≪3310−x2≪31⇒−3≪x∪x≫33(x−2)2≪31⇒1≪x≪3t≪9solutionx=3

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