Question

tìm giá trị lớn nhất

Answer 1

`a)|x|>=0`

`=>|x|+1997>=1997`

`=>A<=1996/1997`

Dấu "=" xảy ra khi `x=0`

`b)|x|>=0`

`=>|x|+1996>=1996`

`=>-(|x|+1996)<=-1996`

`=>B<=-1996/1997`

Dấu "=" xảy ra khi `x=0`.

`c)c=-|x+4/7|+12/19`

Vì `|x+4/7|>=0`

`=>-|x+4/7|<=0`

`=>C<=12/19`

Dấu "=" xảy ra khi `x=-4/7`

<= là giá trị lớn nhất nhé.

Answer 2

a, Ta có : \(\left|x\right|\ge0\forall x\in R\)

\(\Leftrightarrow\left|x\right|+1997\ge1997\forall x\in R\)

\(\Leftrightarrow A=\dfrac{1996}{\left|x\right|+1997}\le\dfrac{1996}{1997}\)

Vậy \(Max_A=\dfrac{1996}{1997}\Leftrightarrow x=0\)

b, Ta có : \(\left|x\right|\ge0\forall x\in R\)

\(\Leftrightarrow\left|x\right|+1996\ge1996\forall x\in R\)

\(\Leftrightarrow B=\dfrac{\left|x\right|+1996}{-1997}\le-\dfrac{1996}{1997}\)

Vậy \(Max_B=-\dfrac{1996}{1997}\Leftrightarrow x=0\)

c, Ta có : \(\left|x+\dfrac{4}{7}\right|\ge0\forall x\in R\)

\(\Leftrightarrow-\left|x+\dfrac{4}{7}\right|\le0\forall x\in R\)

\(\Leftrightarrow\dfrac{12}{19}-\left|x+\dfrac{4}{7}\right|\le\dfrac{12}{19}\forall x\in R\)

Vậy \(Max_C=\dfrac{12}{19}\Leftrightarrow x=-\dfrac{4}{7}\)