{"status": "success", "data": {"description_md": "Real numbers $x$ and $y$ satisfy $x + y = 4$ and $x \\cdot y = -2$. What is the value of$$x + \\frac{x^3}{y^2} + \\frac{y^3}{x^2} + y?$$\n$\\textbf{(A)}\\ 360\\qquad\\textbf{(B)}\\ 400\\qquad\\textbf{(C)}\\ 420\\qquad\\textbf{(D)}\\ 440\\qquad\\textbf{(E)}\\ 480$", "description_html": "<p>Real numbers  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span>  satisfy  <span class=\"katex--inline\">x + y = 4</span>  and  <span class=\"katex--inline\">x \\cdot y = -2</span> . What is the value of <span class=\"katex--display\">x + \\frac{x^3}{y^2} + \\frac{y^3}{x^2} + y?</span> <br/>\n <span class=\"katex--inline\">\\textbf{(A)}\\ 360\\qquad\\textbf{(B)}\\ 400\\qquad\\textbf{(C)}\\ 420\\qquad\\textbf{(D)}\\ 440\\qquad\\textbf{(E)}\\ 480</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": "2020 AMC 10A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p15", "prev": "/problem/20_amc10A_p13"}}