{"status": "success", "data": {"description_md": "Assume that $x_1,x_2,\\ldots,x_7$ are real numbers such that<br>\n$$ \\begin{array}{r} x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1\\,\\,\\,\\,\\,\\,\\,\\, \\\\ 4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12\\,\\,\\,\\,\\, \\\\ 9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123. \\\\ \\end{array} $$Find the value of $$16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7. $$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Assume that <span class=\"katex--inline\">x_1,x_2,\\ldots,x_7</span> are real numbers such that<br/><span class=\"katex--display\"> \\begin{array}{r} x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1\\,\\,\\,\\,\\,\\,\\,\\, \\\\ 4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12\\,\\,\\,\\,\\, \\\\ 9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123. \\\\ \\end{array} </span>Find the value of <span class=\"katex--display\">16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "1989 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p09", "prev": "/problem/89_aime_p07"}}