{"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\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></p>&#10;<p><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>&#10;", "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"}}