Question

Tim gia tri lon nhat :

a, A= 5-| 2x - 1 |

b, B= \(\dfrac{1}{\left|x-1\right|+3}\)

c, C= x +\(\dfrac{1}{2}-\left|x-\dfrac{2}{3}\right|\)

Answer 1

\(A=5-\left|2x-1\right|\le5\)

Dấu "=" xảy ra khi:

\(2x=1\Leftrightarrow x=\dfrac{1}{2}\)

\(B=\dfrac{1}{\left|x-1\right|+3}\le\dfrac{1}{3}\)

Dấu "=" xảy ra khi:

\(x=1\)

\(C=x+\dfrac{1}{2}-\left|x-\dfrac{2}{3}\right|\le\left|x+\dfrac{1}{2}-x-\dfrac{2}{3}\right|=\dfrac{1}{6}\)

Dấu "=" xảy ra khi: \(-\dfrac{1}{2}\le x\le\dfrac{2}{3}\)

Answer 2

Ta có: \(\left|2x-1\right|\le0\) với mọi x

\(\Rightarrow5-\left|2x-1\right|\le5-0\) với mọi x

\(\Leftrightarrow A\le5\)

\(\Rightarrow A_{max}=5\)

Dấu \("="\) xảy ra khi:

\(\left|2x-1\right|=0\\ 2x-1=0\\ 2x=1\\ x=1:2=0,5\)

Vậy A đạt giá trị lớn nhất khi \(x=0,5\)