{"status": "success", "data": {"description_md": "*This is a user suggested problem. The TopsOJ staff thanks and gives full credit to [ Maximilian113](https://www.topsoj.com/users/Maximilian113/profile) for their contribution.*  \n  \n****\n\nSuppose that $a, b, c$ are positive reals such that $a^2+b^2+c^2=18.$ Let $$\\begin{aligned} x &=\\sqrt{a^2+b^2+ab}, \\\\ y &=\\sqrt{b^2+c^2+bc}, \\\\ z &= \\sqrt{c^2+a^2+ca}. \\\\ \\end{aligned}$$ Find the maximum possible value of $$(x+y+z)(-x+y+z)(x-y+z)(x+y-z).$$", "description_html": "<p><em>This is a user suggested problem. The TopsOJ staff thanks and gives full credit to <a href=\"https://www.topsoj.com/users/Maximilian113/profile\"> Maximilian113</a> for their contribution.</em></p>&#10;<hr/>&#10;<p>Suppose that <span class=\"katex--inline\">a, b, c</span> are positive reals such that <span class=\"katex--inline\">a^2+b^2+c^2=18.</span> Let <span class=\"katex--display\">\\begin{aligned} x &amp;=\\sqrt{a^2+b^2+ab}, \\\\ y &amp;=\\sqrt{b^2+c^2+bc}, \\\\ z &amp;= \\sqrt{c^2+a^2+ca}. \\\\ \\end{aligned}</span> Find the maximum possible value of <span class=\"katex--display\">(x+y+z)(-x+y+z)(x-y+z)(x+y-z).</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Nice Algebra", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}