Question

a, tìm x biết: | x-1| + | x+3| = 4

b, tìm x biết: | x² + | 6x - 2| | = x² + 4

c, tìm x biết: |2x +3| - 2| 4 - x| = 5

Answer 1

a) Áp dụng BĐT \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) ta có:

\(\left|x-1\right|+\left|x+3\right|=\left|1-x\right|+\left|x+3\right|\ge\left|1-x+x+3\right|=4\)

Đẳng thức xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}1-x\ge0\\x+3\ge0\end{matrix}\right.\)

\(\Leftrightarrow-3\le x\le1\)

Vậy,..................................................................................................................................