`(3x-4)^2-(x-3)^2-3.(x-2).(2x-1)=0`

2 bình luận về “`(3x-4)^2-(x-3)^2-3.(x-2).(2x-1)=0`”

1. (3x-4)^2-(x-3)^2-3.(x-2).(2x-1)=0

   <=> (3x-4-x+3)(3x-4+x-3)-3.(x-2).(2x-1)=0

   <=> (2x-1)(4x-7)-3.(x-2).(2x-1)=0

   <=> (2x-1)(4x-7-3x+6)=0

   <=> (2x-1)(x-1)=0

   <=> [(2x-1=0),(x-1=0):}

   <=> [(2x=1),(x=1):}

   <=> [(x=1/2),(x=1):}

   Vậy x in {1/2;1}

   Trả lời
2. (3x-4)^2-(x-3)^2-3(x-2)(2x-1)=0

   <=>9x^2-24x+16-(x^2-6x+9)-3(2x^2-5x+2)=0

   <=>9x^2-24x+16-x^2+6x-9-6x^2+15x-6=0

   <=>2x^2-3x+1=0

   <=>x^2-3/2x+1/2=0

   <=>x^2-x-1/2x+1/2=0

   <=>x(x-1)-1/2(x-1)=0

   <=>(x-1)(x-1/2)=0

   <=> \(\left[ \begin{array}{l}x-1=0\\x-\dfrac{1}{2}=0\end{array} \right.\) 

   <=> \(\left[ \begin{array}{l}x=1\\x=\dfrac{1}{2}\end{array} \right.\) 

   Vậy S={1/2;1}

    

   Trả lời