tìm `x:` `(3x-2)^3+(2x-3)^2-(5x-5)^3=0`

1 bình luận về “tìm `x:` `(3x-2)^3+(2x-3)^2-(5x-5)^3=0`”

1. (3x-2)^3+(2x-3)^2-(5x-5)^3=0

   =>27x^3-54x^2+36x-8+4x^2-12x+9-(125x^3-375x^2+375x-125)=0

   =>27x^3+(4x^2-54x^2)+(36x-12x)+(9-8)-125x^3+375x^2-375x+125=0

   =>27x^3-50x^2+24x+1-125x^3+375x^2-375x+125=0

   =>(27x^3-125x^3)+(375x^2-50x^2)+(24x-375x)+(1+125)=0

   =>-98x^3+325x^2-351x+126=0

   =>-(98x^3-325x^2+351x-126)=0

   =>98x^3-325x^2+351x-126=0

   =>(98x^3-178x^2+84x)-(147x^2-267x+126)=0

   =>2x(49x^2-89x+42)-3(49x^2-89x+42)=0

   =>(2x-3)(49x^2-89x+42)=0

   TH1:2x-3=0=>2x=3

   =>x=3/2

   TH2:49x^2-89x+42=0

   =>(7x)^2-2.7x. 89/14+(89/14)^2+311/196=0

   =>(7x-89/14)^2+311/196=0

   Vô lý! (7x-89/14)^2+311/196>0∀x

   =>x in ∅

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