{"status": "success", "data": {"description_md": "Let $a$ and $b$ be the roots of the equation $x^2-mx+2=0$. Suppose that $a+\\frac{1}{b}$ and $b+\\frac{1}{a}$ are the roots of the equation $x^2-px+q=0$. What is $q$?\n\n$\\mathrm{(A) \\ } \\frac{5}{2}\\qquad \\mathrm{(B) \\ } \\frac{7}{2}\\qquad \\mathrm{(C) \\ } 4\\qquad \\mathrm{(D) \\ } \\frac{9}{2}\\qquad \\mathrm{(E) \\ } 8$", "description_html": "<p>Let  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  be the roots of the equation  <span class=\"katex--inline\">x^2-mx+2=0</span> . Suppose that  <span class=\"katex--inline\">a+\\frac{1}{b}</span>  and  <span class=\"katex--inline\">b+\\frac{1}{a}</span>  are the roots of the equation  <span class=\"katex--inline\">x^2-px+q=0</span> . What is  <span class=\"katex--inline\">q</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{5}{2}\\qquad \\mathrm{(B) \\ } \\frac{7}{2}\\qquad \\mathrm{(C) \\ } 4\\qquad \\mathrm{(D) \\ } \\frac{9}{2}\\qquad \\mathrm{(E) \\ } 8</span> </p>\n<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": 3, "problem_name": "2006 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10B_p15", "prev": "/problem/06_amc10B_p13"}}