Tìm x: `x^2(x-2) – 2x^2 + 8x – 8 =0`

2 bình luận về “Tìm x: `x^2(x-2) – 2x^2 + 8x – 8 =0`”

1. x^2( x-2 ) – 2x^2 + 8x – 8 = 0

   <=> x^2( x-2 ) – 2( x^2 – 4x + 4 ) = 0

   <=> x^2( x-2 ) – 2( x-2 )^2 = 0

   <=> ( x-2 )[x^2 – 2( x-2 )] = 0

   <=> ( x-2 )( x^2 – 2x + 4 ) = 0

   => x-2=0 ( do x^2 – 2x + 4 >= 3 \ne 0 )

   <=> x=2

   Vậy x=2

    

   Trả lời
2. x^2(x-2)-2x^2+8x-8=0

   <=>x^3 -2x^2-2x^2+8x-8=0

   <=>x^3-2x^2-2x^2+4x+4x-8=0

   <=>x^2(x-2) -2x(x-2)+4(x-2)=0

   <=>(x^2-2x+4)(x-2)=0

   <=>\(\left[ \begin{array}{l}x^2-2x+4=0\\x-2=0\end{array} \right.\) 

   <=>\(\left[ \begin{array}{l}(x-1)^2=-3 \text{(vô lí với mọi }  x)\\x=2\end{array} \right.\) 

   Vậy x=2

   Trả lời