Question

số các giá trị của x thỏa mãn \(\dfrac{\left|x-7\right|}{\left|x-4\right|}\)=\(\dfrac{\left|x-1\right|}{\left|x-4\right|}\)

Answer 1

\(\dfrac{\left|x-7\right|}{\left|x-4\right|}=\dfrac{\left|x-1\right|}{\left|x-4\right|}\)

Ta xét: \(\left|x-7\right|\ge0;\left|x-4\right|\ge0\)

\(\Rightarrow\dfrac{\left|x-7\right|}{\left|x-4\right|}\ge0\)

Ta lại xét: \(\left|x-1\right|\ge0;\left|x-4\right|\ge0\)

\(\Rightarrow\dfrac{\left|x-1\right|}{\left|x-4\right|}\ge0\)

\(\dfrac{\left|x-7\right|}{\left|x-4\right|}=\dfrac{\left|x-1\right|}{\left|x-4\right|}\)

\(\Rightarrow\dfrac{x-7}{x-4}=\dfrac{x-1}{x-4}\)

\(\Rightarrow x-7=x-1\)

=> \(x\in\varnothing\)