Question

[Nguyễn Quốc Cường]

giúp tui vs đaggggggggg gấp lắm ạ

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(\left|5-\dfrac{2}{3}x\right|>=0\forall x;\left|\dfrac{2}{3}y-4\right|>=0\forall y\)

Do đó: \(\left|5-\dfrac{2}{3}x\right|+\left|\dfrac{2}{3}y-4\right|>=0\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}5-\dfrac{2}{3}x=0\\\dfrac{2}{3}y-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5:\dfrac{2}{3}=\dfrac{15}{2}\\y=4:\dfrac{2}{3}=6\end{matrix}\right.\)

b: \(\left|\dfrac{2}{3}-\dfrac{1}{2}+\dfrac{3}{4}x\right|>=0\forall x;\left|1,5-\dfrac{3}{4}-\dfrac{3}{2}y\right|>=0\forall y\)

Do đó: \(\left\{{}\begin{matrix}\dfrac{2}{3}-\dfrac{1}{2}+\dfrac{3}{4}x=0\\1,5-\dfrac{3}{4}-\dfrac{3}{2}y=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{3}{4}x=-\dfrac{2}{3}+\dfrac{1}{2}=-\dfrac{1}{6}\\\dfrac{3}{2}y=1,5-\dfrac{3}{4}=\dfrac{3}{2}-\dfrac{3}{4}=\dfrac{3}{4}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-\dfrac{1}{6}:\dfrac{3}{4}=-\dfrac{1}{6}\cdot\dfrac{4}{3}=\dfrac{-4}{18}=-\dfrac{2}{9}\\y=\dfrac{1}{2}\end{matrix}\right.\)

c: \(\left|x-2020\right|>=0\forall x;\left|y-2021\right|>=0\forall y\)

Do đó: \(\left|x-2020\right|+\left|y-2021\right|>=0\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-2020=0\\y-2021=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2020\\y=2021\end{matrix}\right.\)

d: \(\left|x-y\right|>=0\forall x,y\)

\(\left|y+\dfrac{21}{10}\right|>=0\forall y\)

Do đó: \(\left|x-y\right|+\left|y+\dfrac{21}{10}\right|>=0\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-y=0\\y+\dfrac{21}{10}=0\end{matrix}\right.\Leftrightarrow x=y=-\dfrac{21}{10}\)