https://minidemo.mathonline.se/index.php?action=history&feed=atom&title=1.1_L%C3%B6sning_2
1.1 Lösning 2 - Versionshistorik
2026-06-29T19:56:47Z
Versionshistorik för denna sida på wikin
MediaWiki 1.23.1
https://minidemo.mathonline.se/index.php?title=1.1_L%C3%B6sning_2&diff=603&oldid=prev
Taifun: Created page with "<math>\begin{align} 2\,\sqrt{x} - x & = 1 & | \;\; + x \\ 2\,\sqrt{x} & = x + 1 & | \; (\;\;\;)^2 \\ ..."
2010-11-24T08:02:33Z
<p>Created page with "<math>\begin{align} 2\,\sqrt{x} - x & = 1 & | \;\; + x \\ 2\,\sqrt{x} & = x + 1 & | \; (\;\;\;)^2 \\ ..."</p>
<p><b>Ny sida</b></p><div><math>\begin{align} 2\,\sqrt{x} - x & = 1 & | \;\; + x \\<br />
2\,\sqrt{x} & = x + 1 & | \; (\;\;\;)^2 \\<br />
4\,x & = (x + 1)^2 \\<br />
4\,x & = x^2 + 2 x + 1 & | -4x \\<br />
0 & = x^2 - 2 x + 1 \\<br />
x_{1,2} & = 1 \pm \sqrt{1 - 1} \\<br />
x & = 1 \\<br />
\end{align}</math><br />
<br />
Prövning:<br />
<br />
VL: <math> 2\,\sqrt{1} - 1 = 2 - 1 = 1 </math><br />
<br />
HL: <math> \displaystyle 1 </math><br />
<br />
VL = HL <math> \Rightarrow\, x = 1 </math> är rotekvationens lösning.</div>
Taifun