tìm x biết a) |-3+x|= |2x-1| b) (x-5)^2=(2x-1)^2

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1. Đáp án:

    #`|a|=|b|↔(|a|)^2-(|b|)^2`

   # `a^2-b^2=(a-b)(a+b)`

   Giải thích các bước giải:

   `a,|-3+x|=|2x-1|`

   `⇔(|-3+x|)^2=(|2x-1|)^2`

    `⇔(x-3)^2-(2x-1)^2`

   `⇔(x-3-2x+1)(x-3+2x-1)=0`

   `⇔(-x-2)(3x-4)=0`

   ⇔\(\left[ \begin{array}{l}-x-2=0\\3x-4=0\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=-2\\x=\dfrac{4}{3}\end{array} \right.\) 

   Vậy `x=-2;x=4/3`

   `b,(x-5)^2=(2x-1)^2`

   `⇔(x-5)^2-(2x-1)^2=0`

   `⇔(x-5+2x-1)(x-5-2x+1)=0`

   `⇔(3x-6)(-x-4)=0`

   ⇔\(\left[ \begin{array}{l}3x-6=0\\-x-4=0\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=2\\x=-4\end{array} \right.\) 

   Vậy `x=2;x=-4`

   Trả lời

2. Đáp án + Giải thích các bước giải:

   `a//|-3+x|=|2x-1|`

   `=>` \(\left[ \begin{array}{l}-3+x=2x-1\\-3+x=-2x+1\end{array} \right.\) 

   `=>` \(\left[ \begin{array}{l}x-2x=3-1\\x+2x=3+1\end{array} \right.\) 

   `=>` \(\left[ \begin{array}{l}-x=2\\3x=4\end{array} \right.\) 

   `=>` \(\left[ \begin{array}{l}x=-2\\x=\frac{4}{3}\end{array} \right.\) 

   Vậy `x∈{-2;(4)/(3)}`

   `b//(x-5)^{2}=(2x-1)^{2}`

   `⇒` \(\left[ \begin{array}{l}x-5=2x-1\\x-5=-2x+1\end{array} \right.\) 

   `⇒` \(\left[ \begin{array}{l}x-2x=5-1\\x+2x=5+1\end{array} \right.\) 

   `⇒` \(\left[ \begin{array}{l}-x=4\\3x=6\end{array} \right.\) 

   `⇒` \(\left[ \begin{array}{l}x=-4\\x=2\end{array} \right.\) 

   Vậy `x∈{-4;2}`

   Trả lời