giai hpt 2^x+2^y<=1 x+y>=-2

Đáp án:

\(\left( {x;y} \right) = \left( { - 1; - 1} \right)\)

Giải thích các bước giải:

$$\eqalign{ & \left\{ \matrix{ {2^x} + {2^y} \le 1\,\,\,\,\left( 1 \right) \hfill \cr x + y \ge - 2\,\,\,\,\left( 2 \right) \hfill \cr} \right. \cr & Do\,\,x,\,\,y\,\,binh\,\,dang. \cr & Khong\,\,mat\,\,tinh\,\,tong\,\,quat\,\,ta\,\,gia\,\,su\,\,x \le y \cr & \Rightarrow {2^x} \le {2^y} \cr & \Rightarrow {2^x} + {2^y} \le {2^y} + {2^y} = {2.2^y} = {2^{y + 1}} \le 1 \cr & \Rightarrow y + 1 \le 0 \Leftrightarrow y \le - 1 \cr & \Leftrightarrow x \le y \le - 1 \cr & \Leftrightarrow x + y \le - 2 \cr & Ma\,\,x + y \ge - 2 \cr & \Rightarrow x + y = - 2 \cr & Dau\,\,'' = ''\,\,xay\,\,ra \Leftrightarrow \left\{ \matrix{ x = y \hfill \cr y = - 1 \hfill \cr} \right. \Leftrightarrow x = y = - 1 \cr & Vay\,\,nghiem\,\,cua\,hpt\,\,la\,\,\left( {x;y} \right) = \left( { - 1; - 1} \right) \cr} $$