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1.1 Lösning 3a - Versionshistorik
2026-05-28T23:22:21Z
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Taifun den 22 augusti 2018 kl. 23.11
2018-08-22T23:11:47Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 22 augusti 2018 kl. 23.11</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 14:</td>
<td colspan="2" class="diff-lineno">Rad 14:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Först prövar vi <math> x_1 = 2 </math>:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Först prövar vi <math> x_1 = 2 </math>:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>VL: <math> \displaystyle 2 </math></div></td><td class='diff-marker'>+</td><td style="color:black; 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>VL<ins class="diffchange diffchange-inline"><span style="color</ins>:<ins class="diffchange diffchange-inline">black">:</span> </ins><math> <ins class="diffchange diffchange-inline">\;\; </ins>\displaystyle 2 </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>HL: <math> \sqrt{2+7} - 1 = \sqrt{9} - 1 = 3 - 1 = 2 </math></div></td><td class='diff-marker'>+</td><td style="color:black; 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>HL<ins class="diffchange diffchange-inline"><span style="color</ins>:<ins class="diffchange diffchange-inline">black">:</span> </ins><math> <ins class="diffchange diffchange-inline">\;\; </ins>\sqrt{2+7} - 1 = \sqrt{9} - 1 = 3 - 1 = 2 </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>VL = HL <math> \Rightarrow\; x_1 = 2 </math> är en sann rot.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>VL = HL <math> \Rightarrow\; x_1 = 2 </math> är en sann rot.</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Rad 22:</td>
<td colspan="2" class="diff-lineno">Rad 22:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Sedan prövar vi roten <math> x_2 = -3 </math>:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Sedan prövar vi roten <math> x_2 = -3 </math>:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>VL: <math> \displaystyle -3 </math></div></td><td class='diff-marker'>+</td><td style="color:black; 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>VL<ins class="diffchange diffchange-inline"><span style="color</ins>:<ins class="diffchange diffchange-inline">black">:</span> </ins><math> <ins class="diffchange diffchange-inline">\;\; </ins>\displaystyle -3 </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>HL: <math> \sqrt{-3+7} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 </math></div></td><td class='diff-marker'>+</td><td style="color:black; 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>HL<ins class="diffchange diffchange-inline"><span style="color</ins>:<ins class="diffchange diffchange-inline">black">:</span> </ins><math> <ins class="diffchange diffchange-inline">\;\; </ins>\sqrt{-3+7} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>VL <math> \not= </math> HL <math> \Rightarrow\; x_2 = -3 </math> är en falsk rot.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>VL <math> \not= </math> HL <math> \Rightarrow\; x_2 = -3 </math> är en falsk rot.</div></td></tr>
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Taifun
https://matte3c.mathonline.se/index.php?title=1.1_L%C3%B6sning_3a&diff=2006&oldid=prev
Taifun: Created page with "<math>\begin{align} x & = \sqrt{x+7} - 1 & & | \;\; + 1 \\ x + 1 & = \sqrt{x+7} & & | \; (\;\;\;)^2 \\ ..."
2011-01-23T20:52:23Z
<p>Created page with "<math>\begin{align} x & = \sqrt{x+7} - 1 & & | \;\; + 1 \\ x + 1 & = \sqrt{x+7} & & | \; (\;\;\;)^2 \\ ..."</p>
<p><b>Ny sida</b></p><div><math>\begin{align} x & = \sqrt{x+7} - 1 & & | \;\; + 1 \\<br />
x + 1 & = \sqrt{x+7} & & | \; (\;\;\;)^2 \\<br />
(x + 1)^2 & = x + 7 \\<br />
x^2 + 2 x + 1 & = x + 7 & & | -x-7 \\<br />
x^2 + x - 6 & = 0 \\<br />
x_{1,2} & = -0,5 \pm \sqrt{0,25 + 6} \\<br />
x_{1,2} & = -0,5 \pm 2,5 \\<br />
x_1 & = 2 \\<br />
x_2 & = -3 \\<br />
\end{align}</math><br />
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Prövning:<br />
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Först prövar vi <math> x_1 = 2 </math>:<br />
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VL: <math> \displaystyle 2 </math><br />
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HL: <math> \sqrt{2+7} - 1 = \sqrt{9} - 1 = 3 - 1 = 2 </math><br />
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VL = HL <math> \Rightarrow\; x_1 = 2 </math> är en sann rot.<br />
<br />
Sedan prövar vi roten <math> x_2 = -3 </math>:<br />
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VL: <math> \displaystyle -3 </math><br />
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HL: <math> \sqrt{-3+7} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 </math><br />
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VL <math> \not= </math> HL <math> \Rightarrow\; x_2 = -3 </math> är en falsk rot.<br />
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Svar: Ekvationen<br />
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:<math> x = \sqrt{x+7} - 1 </math><br />
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har den enda lösningen<br />
<br />
::<math> \displaystyle x = 2 </math></div>
Taifun