Question

Tìm x và y sao cho:

a) |x+25|+|-y+5|=0

b) |x-40|+|x-y+10|<_ 0

<_ là lớn hơn hoặc =

giúp mk nhá

Answer 1

a, \(\left|x+25\right|+\left|-y+5\right|=0\)

Mà \(\left\{{}\begin{matrix}\left|x+25\right|\ge0\\\left|-y+5\right|\ge0\end{matrix}\right.\Rightarrow\left|x+25\right|+\left|-y+5\right|\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+25\right|=0\\\left|-y+5\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-25\\y=5\end{matrix}\right.\)

Vậy x = -25 và y = 5

b, \(\left|x-40\right|+\left|x-y+10\right|\le0\)

Mà \(\left|x-40\right|+\left|x-y+10\right|\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x-40\right|=0\\\left|x-y+10\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=40\\y=50\end{matrix}\right.\)

Vậy x = 40 và y = 50

Answer 2

\(\left|x+25\right|+\left|-y+5\right|=0\)

\(\left\{{}\begin{matrix}\left|x+25\right|\ge0\\\left|-y+5\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x+25\right|+\left|-y+5\right|\ge0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left|x+25\right|=0\Rightarrow x=25\\\left|-y+5\right|=0\Rightarrow-y=-5\Rightarrow y=5\end{matrix}\right.\)

\(\left|x-40\right|+\left|x-y+10\right|\le0\)

\(\left\{{}\begin{matrix}\left|x-40\right|\ge0\\\left|x-y+10\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x-40\right|+\left|x-y+10\right|\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left|x-40\right|+\left|x-y+10\right|\le0\\\left|x-40\right|+\left|x-y+10\right|\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x-40\right|+\left|x-y+10\right|=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x-40\right|=0\Rightarrow x=40\\\left|x-y+10\right|=0\Rightarrow x-y=-10\Rightarrow y=50\end{matrix}\right.\)