Question

Tìm x,y,z ∈ Q :

|x+\(\dfrac{2}{3}\)|+|y-\(\dfrac{3}{4}\)|+|z-5|=0

các bạn giúp mình nha, mình cảm ơn nhiều

Answer 1

\(\left|x+\dfrac{2}{3}\right|+\left|y-\dfrac{3}{4}\right|+\left|z-5\right|=0\)

\(\left\{{}\begin{matrix}\left|x+\dfrac{2}{3}\right|\ge0\forall x\\\left|y-\dfrac{3}{4}\right|\ge0\forall y\\\left|z-5\right|\ge0\forall z\end{matrix}\right.\) \(\Rightarrow\left|x+\dfrac{2}{3}\right|+\left|y-\dfrac{3}{4}\right|+\left|z-5\right|\ge0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left|x+\dfrac{2}{3}\right|=0\\\left|y-\dfrac{3}{4}\right|=0\\\left|z-5\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{3}\\y=\dfrac{3}{4}\\z=5\end{matrix}\right.\)