Question

Tìm GTNN

a. \(\mid x-7\mid\) + \(\mid x+5\mid\)

b. \((2x-1)^2 -3\mid2x-1\mid +2\)

c.\(\mid x^2 + x + 1\mid + \mid x^2 +x -12\mid\)

Answer 1

a) Bạn adct \(\left|x\right|+\left|y\right|\ge\left|x+y\right|\)

Ta cóA= \(\left|x-7\right|+\left|x+5\right|=\left|7-x\right|+\left|x+5\right|\ge\left|7-x+x+5\right|\)

=> \(\left|7-x\right|+\left|x+5\right|\ge12\) vậy minA=12

Answer 2

b)Ta có \(\left(2x-1\right)^2-3\left|2x-1\right|+2=\left|2x-1\right|^2-2\left|2x-1\right|.\frac{3}{2}+\frac{9}{4}-\frac{1}{4}=\left(\left|2x-1\right|-\frac{3}{2}\right)^2-\frac{1}{4}\)=>minA=-1/4

Answer 3

còn câu c thì bạn làm giống câu a nhé