{"status": "success", "data": {"description_md": "Under what conditions is $\\sqrt{a^2+b^2}=a+b$ true, where $a$ and $b$ are real numbers?\n\n$\\textbf{(A) }$ It is never true.\n\n$\\textbf{(B) }$ It is true if and only if $ab=0$.\n\n$\\textbf{(C) }$ It is true if and only if $a+b\\ge 0$.\n\n$\\textbf{(D) }$ It is true if and only if $ab=0$ and $a+b\\ge 0$.\n\n$\\textbf{(E) }$ It is always true.\n___\nFull 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>Under what conditions is  <span class=\"katex--inline\">\\sqrt{a^2+b^2}=a+b</span>  true, where  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are real numbers?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }</span>  It is never true.</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(B) }</span>  It is true if and only if  <span class=\"katex--inline\">ab=0</span> .</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(C) }</span>  It is true if and only if  <span class=\"katex--inline\">a+b\\ge 0</span> .</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(D) }</span>  It is true if and only if  <span class=\"katex--inline\">ab=0</span>  and  <span class=\"katex--inline\">a+b\\ge 0</span> .</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(E) }</span>  It is always true.</p>&#10;<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": 2, "problem_name": "2021 AMC 12A Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p03", "prev": "/problem/21_amc12A_p01"}}