Question

Tìm x,y:\(\left|x-1\right|+\left|x-2\right|+\left|y-3\right|+\left|x-4\right|=3\)

Answer 1

Lời giải:
Áp dụng BĐT $|a|+|b|\geq |a+b|$ ta có:

$|x-1|+|x-4|=|x-1|+|4-x|\geq |x-1+4-x|=3$

$|x-2|+|y-3|\geq 0$

$\Rightarrow |x-1|+|x-2|+|y-3|+|x-4|\geq 3$

Dấu "=" xảy ra khi:
\(\left\{\begin{matrix} (x-1)(4-x)\geq 0\\ x-2=0\\ y-3=0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=2\\ y=3\end{matrix}\right.\)