?? ch11_2_1.htm
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<TITLE> 一般方程式 </TITLE>
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<H1>11.2.1 一般方程式</H1>
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以符號數學解一般方程式和聯立方程式的語法如下：
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<FONT COLOR=#FF0000 FACE="Times New Roman">solve(f) </FONT>解符號方程式<FONT COLOR=#FF0000 FACE="Times New Roman">f</FONT>。
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<FONT COLOR=#FF0000 FACE="Times New Roman">solve(f1,</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">厎</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">,fn)
</FONT><FONT COLOR=#FF0000>解由</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">f1,</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">厎</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">,fn</FONT><FONT COLOR=#FF0000>組成的聯立方程式。
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<FONT COLOR=#FF0000>我們先定義以下的方程式：</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq1 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x-3=4</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;
% </FONT><FONT COLOR=#FF0000>注意也可寫成'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">eq1=x-7</FONT><FONT COLOR=#FF0000>'</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq2 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x*2-x-6=0</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;
% </FONT><FONT COLOR=#FF0000>注意也可寫成'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">eq2=x*2-x-6</FONT><FONT COLOR=#FF0000>'</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq3 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x2+2*x+4=0</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq4 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">3*x+2*y-z=10</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq5 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">-x+3*y+2*z=5</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>eq6 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">x-y-z=-1</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>solve(eq1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">7</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>solve(eq2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">[[3],[-2]]</FONT><FONT COLOR=#FF0000>'
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">% </FONT><FONT COLOR=#FF0000>原方程式有二個根</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">3,
-2</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>solve(eq3)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">[[-1+I*3^(1/2)],[-1-I*3^(1/2)]]</FONT><FONT COLOR=#FF0000>'
</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">% </FONT><FONT COLOR=#FF0000>注意實根和虛根的表示式</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>solve(eq4,eq5,eq6)
% </FONT><FONT COLOR=#FF0000>解三個聯立方程式</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">x = -2, y = 5, z =
-6</FONT><HR>
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