Let $A=\{(x,y)\in\mathbf R imes\mathbf R:|x+y|\ge3\}$ and $B=\{(x,y)\in\mathbf R imes\mathbf R:|x|+|y|\le3\}$. If $C=\{(x,y)\in A\cap B:x=0 ext{ or }y=0\}$, then $\sum_{(x,y)\in C}|x+y|$ is :

Question

Let $A=\{(x,y)\in\mathbf R	imes\mathbf R:|x+y|\ge3\}$ and $B=\{(x,y)\in\mathbf R	imes\mathbf R:|x|+|y|\le3\}$. If $C=\{(x,y)\in A\cap B:x=0	ext{ or }y=0\}$, then $\sum_{(x,y)\in C}|x+y|$ is :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] On $x=0$: $|y|\ge3$ and $|y|\le3$ give $y=\pm3$. On $y=0$: $x=\pm3$. So $C=\{(0,\pm3),(\pm3,0)\}$ and each point has $|x+y|=3$. Sum $=12$. Answer (4).

Q. Let $A=\{(x,y)\in\mathbf R\times\mathbf R:|x+y|\ge3\}$ and $B=\{(x,y)\in\mathbf R\times\mathbf R:|x|+|y|\le3\}$. If $C=\{(x,y)\in A\cap B:x=0\text{ or }y=0\}$, then $\sum_{(x,y)\in C}|x+y|$ is :

Explanation

Reviewed by Dr. Abubacker

Want to attempt the full paper?