https://artofproblemsolving.com/wiki/index.php?title=1958_AHSME_Problems/Problem_11&feed=atom&action=history
1958 AHSME Problems/Problem 11 - Revision history
2024-03-29T07:06:50Z
Revision history for this page on the wiki
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Mathgeek2006: /* Problem */
2015-03-14T03:09:15Z
<p><span dir="auto"><span class="autocomment">Problem</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 03:09, 14 March 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Problem==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Problem==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The number of roots satisfying the equation <math> \sqrt{5 <del class="diffchange diffchange-inline">\minus{} </del>x} <del class="diffchange diffchange-inline">\equal{} </del>x\sqrt{5 <del class="diffchange diffchange-inline">\minus{} </del>x}</math> is:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The number of roots satisfying the equation <math> \sqrt{5 <ins class="diffchange diffchange-inline">- </ins>x} <ins class="diffchange diffchange-inline">= </ins>x\sqrt{5 <ins class="diffchange diffchange-inline">- </ins>x}</math> is:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> \textbf{(A)}\ \text{unlimited}\qquad  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> \textbf{(A)}\ \text{unlimited}\qquad  </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(D)}\ 1\qquad  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(D)}\ 1\qquad  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(E)}\ 0</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(E)}\ 0</math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
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Mathgeek2006
https://artofproblemsolving.com/wiki/index.php?title=1958_AHSME_Problems/Problem_11&diff=64243&oldid=prev
Timneh: /* See also */
2014-10-03T10:08:00Z
<p><span dir="auto"><span class="autocomment">See also</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:08, 3 October 2014</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME box|year=1958|num-b=10|num-a=12}}</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME <ins class="diffchange diffchange-inline">50p </ins>box|year=1958|num-b=10|num-a=12}}</div></td></tr>
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Timneh
https://artofproblemsolving.com/wiki/index.php?title=1958_AHSME_Problems/Problem_11&diff=58609&oldid=prev
Dasobson: Created page with "==Problem== The number of roots satisfying the equation <math> \sqrt{5 \minus{} x} \equal{} x\sqrt{5 \minus{} x}</math> is: <math> \textbf{(A)}\ \text{unlimited}\qquad \textbf..."
2014-01-04T04:02:00Z
<p>Created page with "==Problem== The number of roots satisfying the equation <math> \sqrt{5 \minus{} x} \equal{} x\sqrt{5 \minus{} x}</math> is: <math> \textbf{(A)}\ \text{unlimited}\qquad \textbf..."</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
The number of roots satisfying the equation <math> \sqrt{5 \minus{} x} \equal{} x\sqrt{5 \minus{} x}</math> is:<br />
<br />
<math> \textbf{(A)}\ \text{unlimited}\qquad <br />
\textbf{(B)}\ 3\qquad <br />
\textbf{(C)}\ 2\qquad <br />
\textbf{(D)}\ 1\qquad <br />
\textbf{(E)}\ 0</math><br />
<br />
<br />
==Solution==<br />
<br />
Solve the equation for x.<br />
<br />
<cmath>\sqrt{5-x}=x\sqrt{5-x}</cmath><br />
<br />
<cmath>x\sqrt{5-x} - \sqrt{5-x} = 0</cmath><br />
<br />
<cmath>(x-1)\sqrt{5-x}=0</cmath><br />
<br />
<cmath>x=1,5</cmath><br />
<br />
There are two solutions <math>\to \boxed{\textbf{(C)}}</math><br />
<br />
<br />
==See also==<br />
<br />
{{AHSME box|year=1958|num-b=10|num-a=12}}<br />
{{MAA Notice}}</div>
Dasobson