Lösung Gleichungen gemeinsamer Form
Zuletzt geändert von akukin am 2025/08/11 15:28
\(e^{2x}-4e^x+3=0\)
\(u:=e^x\)
⬊\(x^{2e}-4x^e+3=0\)
\(u:=x^e\)
🠗\(x^{-2}-4x^{-1}+3=0\)
\(u:=x^{-1}\)
⬋\(u^2-4u+3=0\)
\(u_{1,2}=\frac{4\pm \sqrt{16-12}}{2}\)
\(u_1=3 \quad;\quad u_2=1\)⬋
\(e^x:=u\)\(x_{1}=ln(3)\)
\(x_{2}=ln(1)=0\)
🠗
\(x^e:=u\)\(x_{1}=\sqrt[e]{3}\)
\(x_{2}=\sqrt[e]{1}=1\)
⬊
\(x^{-1}:=u\)\(x_{1}=\frac{1}{3}\)
\(x_{2}=1\)
\(x^{-2}-3x^{-1}=0\)
\(u:=x^{-1}\)
⬊\(x^{2e}-3x^e=0\)
\(u:=x^e\)
🠗\(e^{2x}-3e^x=0\)
\(u:=e^x\)
⬋\(u^2-3u=0\)
\(u\cdot (u-3)=0\)
\(u_1=0 \quad;\quad u_2=3 \)⬋
\(x^{-1}:=u\)\(x_{1}=\frac{1}{3}\)
keine weitere Lösung
🠗
\(x^e:=u\)\(x_{1}=\sqrt[e]{3}\)
\(x_{2}=\sqrt[e]{0}=0\)
⬊
\(e^x:=u\)\(x_{1}=ln(3)\)
keine weitere Lösung\(x^{-2}-2x^{-1}+3=0\)
\(u:=x^{-1}\)
⬊\(x^{2e}-2x^e+3=0\)
\(u:=x^e\)
🠗\(e^{2x}-2e^x+3=0\)
\(u:=e^x\)
⬋\(u^2-2u+3=0\) \(u_{1,2}=\frac{2\pm \sqrt{4-12}}{2}\)
keine Lösungen