{"status": "success", "data": {"description_md": "Let $f(x) = x^2 + 6x + 1$, and let $R$ denote the set of points $(x,y)$ in the coordinate plane such that \n\n$$f(x) + f(y) \\le 0 \\qquad \\text{and} \\qquad f(x)-f(y) \\le 0$$<br>The area of $R$ is closest to \n\n$\\mathrm{(A)}\\ 21<br>\\qquad\\mathrm{(B)}\\ 22<br>\\qquad\\mathrm{(C)}\\ 23<br>\\qquad\\mathrm{(D)}\\ 24<br>\\qquad\\mathrm{(E)}\\ 25$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">f(x) = x^2 + 6x + 1</span> , and let  <span class=\"katex--inline\">R</span>  denote the set of points  <span class=\"katex--inline\">(x,y)</span>  in the coordinate plane such that</p>&#10;<p> <span class=\"katex--display\">f(x) + f(y) \\le 0 \\qquad \\text{and} \\qquad f(x)-f(y) \\le 0</span> <br/>The area of  <span class=\"katex--inline\">R</span>  is closest to</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 21\\qquad\\mathrm{(B)}\\ 22\\qquad\\mathrm{(C)}\\ 23\\qquad\\mathrm{(D)}\\ 24\\qquad\\mathrm{(E)}\\ 25</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2002 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/02_amc12B_p24"}}