Question

Tìm x, y biết :

                   |x + 2| + |x - 1| = 3 - (y + 2)²

Answer 1

Ta có \(\left|x+2\right|+\left|x-1\right|=\left|x+2\right|+\left|1-x\right|\ge\left|x+2+1-x\right|=3\)

\(3-\left(y+2\right)^2\le3\) \(\Rightarrow VT\ge VP\) Đẳng thức xảy ra \(\Leftrightarrow\left[{}\begin{matrix}\left(x+2\right)\left(1-x\right)\ge0\\\left(y+2\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}-2\le x\le1\\y=-2\end{matrix}\right.\)

\(\Rightarrow x\in\left\{-2;-1;0;1\right\}\) và y=-2 

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