Question

[CuXi Girl]

Tìm x thuộc Z:

I x+1 I - I x-3 I= 0

Answer 1

[Phùng Thiên Phước]

Ta có\(\left|x+1\right|-\left|x-3\right|=0\)
   \(\Rightarrow\orbr{\begin{cases}\left(x+1\right)-\left(x-3\right)=0\\\left(x+1\right)+\left(x-3\right)=0\end{cases}}\)

Nếu \(\left(x+1\right)-\left(x-3\right)=0\)
   \(\Rightarrow x+1=x-3\)\(\Rightarrow x=x-4\)
   \(\Rightarrow x\)không tồn tại.

Nếu \(\left(x+1\right)+\left(x-3\right)=0\)
   \(\Rightarrow x+1=-\left(x-3\right)=3-x\)
   \(\Rightarrow2\left(x+1\right)=\left(x+1\right)+\left(x+1\right)=\left(x+1\right)+\left(3-x\right)=x+1+3-x=4\)
   \(\Rightarrow x+1=\frac{4}{2}=2\)
   \(\Rightarrow x=2-1=1\)

Vậy \(x=2\)

Answer 2

[ganghochanh]

lx+1l - lx-3l=0

 x=2;x=6

Thay số:l2+1l - l6 - 3l=0

  Vậy x=2;x=3