2.46. Sử dụng tính chất $\left |a+b \right |\leq\left | a\right |+\left ...

{
"content1": "Sử dụng tính chất $\left |a+b  \right | \leq \left |  a\right |+\left |  b\right |$, ta có $\left |  x-1\right |+\left |x-3  \right | \leq \left |  x-1+x-3\right |$",
"content2": "Simplifying the right side, we get $\left |  x-1\right |+\left |x-3  \right | \leq \left |  2x-4\right |$",
"content3": "Since $\left |  x-1\right |+\left |x-3  \right |=\sqrt{2}$, we have $\sqrt{2} \leq \left |  2x-4\right |$",
"content4": "This implies $-\sqrt{2} \leq 2x-4 \leq \sqrt{2}$",
"content5": "Solving the inequalities $-\sqrt{2} \leq 2x-4$ and $2x-4 \leq \sqrt{2}$, we find that there is no real number x that satisfies the given equation",
"content6": "Therefore, there does not exist a real number x that satisfies $\left |  x-1\right |+\left |x-3  \right |=\sqrt{2}$"
}