((x-3)^4) – 3*(x^2 – 6*x + 10) = 1 Giải Pt giúp mình với a

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1. `(x^4−12x^3+54x^2−108x+81)−3(x^2−6x+10)−1=0` `(x^4−12x^3+54x^2−108x+81)−(3x^2−18x+30)−1=0`

   `(x^4−12x^3+51x^2−90x+51)−1=0`

   `x^4−12x^3+51x^2−90x+50=0`

   `x^4-x^3-11x^3+11x^2+40x^2-40x-50x+50=0`

   `x^3(x-1)-11x^2(x-1)+40x(x-1)-50(x-1)=0`

   `(x^3-11x^2+40x-50)(x-1)=0`

   `(x^3-5x^2-6x^2+30x+10x-50)(x-1)=0`

   `[x^2(x-5)-6x(x-5)+10(x-5)](x-1)=0`

   `(x^2-6x+10)(x-5)(x-1)=0`

   TH1: `x^2-6x+10 =0 `

   ⇔`x^2-6x+9+1=0`

   ⇔`(x-3)^2=-1 `( Vô lý )

   TH2:` x-5=0`

   ⇔`x=5`

   TH3:`x-1=0`

   ⇔`x=1`

     

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2. Đáp án:

    

   Giải thích các bước giải:

   x 4 − 12 x 3 + 54 x 2 − 108 x + 81 ) − 3 ( x 2 − 6 x + 10 ) − 1 = 0

   ( x 4 − 12 x 3 + 54 x 2 − 108 x + 81 ) − ( 3 x 2 − 18 x + 30 ) − 1 = 0

   ( x 4 − 12 x 3 + 51 x 2 − 90 x + 51 ) − 1 = 0

   x 4 − 12 x 3 + 51 x 2 − 90 x + 50 = 0 x 4 − x 3 − 11 x 3 + 11 x 2 + 40 x 2 − 40 x − 50 x + 50 = 0

   x 3 ( x − 1 ) − 11 x 2 ( x − 1 ) + 40 x ( x − 1 ) − 50 ( x − 1 ) = 0

   ( x 3 − 11 x 2 + 40 x − 50 ) ( x − 1 ) = 0

   ( x 3 − 5 x 2 − 6 x 2 + 30 x + 10 x − 50 ) ( x − 1 ) = 0

   [ x 2 ( x − 5 ) − 6 x ( x − 5 ) + 10 ( x − 5 ) ] ( x − 1 ) = 0

   ( x 2 − 6 x + 10 ) ( x − 5 ) ( x − 1 ) = 0

   trường hợp1: x 2 − 6 x + 10 = 0 ⇔ x 2 − 6 x + 9 + 1 = 0 ⇔ ( x − 3 ) 2 = − 1 ( Vô lý )

   trường hợp2: x − 5 = 0 ⇔ x = 5

   trường hợp 3: x − 1 = 0 ⇔ x = 1

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