尧驰比值方程组

尧驰比值方程组
第一类:
X1:X2:X3:X4:...:Xn＝a1:a2:a3:a4:...:an
X1＋X2十X3十X4十...十Xn＝a
求:X1，X2，X3，X4，...Xn
解:
X1＝aa1／(a1十a2十a3十...an)，
X2＝aa2／(a1十a2十a3十...an)，
X3＝aa3／(a1十a2十a3十...an)，
...，
Xn＝aan／(a1十a2十a3十...an)
第二类:
X1:X2:X3:X4:...:Xn＝a1:a2:a3:a4:...:an
X1X2X3X4...Xn＝a
求:X1，X2，X3，X4，...Xn
解:
＜一＞当a＞0，
X1＝a1(a/la1a2a3...anl)^(1／n)
X2＝a2(a/la1a2a3...anl^(1／n)
X3＝a3(a/la1a2a3...anl)^(1／n)
...
Xn＝an(a/la1a2a3...anl)^(1／n)
＜二＞当a＜0
X1＝a1(一a/la1a2a3...anl)^(1／n)
X2＝a2(一a/la1a2a3...anl)^(1／n)
X3＝a3(一a/la1a2a3...anl)^(1／n)
...
Xn＝an(一a/la1a2a3...anl)^(1／n)
第三类:
X1:X2:X3:X4:...:Xn＝a1:a2:a3:a4:...:an
X1(X2十X3十X4...Xn)十X2(X3十X4十X5...Xn)十X3(X4十X5十X6...十Xn)十...十X(n一1)Xn＝a
求:X1，X2，X3，X4，...Xn
解:＜一＞a＞0
X1＝a1(a/la1(a2十a3十...十an)十a2(a3十a4十a5十...十an)十...十a(n一1)anl)^(1／2)
X2＝a2(a/la1(a2十a3十...十an)十a2(a3十a4十a5十...十an)十...十a(n一1)anl)^(1／2)
X3＝a3(a/la1(a2十a3十...十an)十a2(a3十a4十a5十...十an)十...十a(n一1)anl)^(1／2)
...
Xn＝an(a/la1(a2十a3十...十an)十a2(a3十a4十a5十...十an)十...十a(n一1)anl)^(1／2)
＜二＞a＜0
X1＝a1(一a/la1(a2十a3十...十an)十a2(a3十a4十a5

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