{"status": "success", "data": {"description_md": "The real number $x$ satisfies the equation $x+\\frac{1}{x} = \\sqrt{5}$. What is the value of $x^{11}-7x^{7}+x^3?$\n\n$\\textbf{(A)} ~-1 \\qquad\\textbf{(B)} ~0 \\qquad\\textbf{(C)} ~1 \\qquad\\textbf{(D)} ~2 \\qquad\\textbf{(E)} ~\\sqrt{5}$", "description_html": "<p>The real number  <span class=\"katex--inline\">x</span>  satisfies the equation  <span class=\"katex--inline\">x+\\frac{1}{x} = \\sqrt{5}</span> . What is the value of  <span class=\"katex--inline\">x^{11}-7x^{7}+x^3?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~-1 \\qquad\\textbf{(B)} ~0 \\qquad\\textbf{(C)} ~1 \\qquad\\textbf{(D)} ~2 \\qquad\\textbf{(E)} ~\\sqrt{5}</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": "2021 AMC 10B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p16", "prev": "/problem/21_amc10B_p14"}}