求解多元多次方程组
0.5325=Q/(2512*N.^0.5*M.^0.5)*exp{-16.81/N-3.0625/M}
0.4947=Q/(2512*N.^0.5*M.^0.5)*exp{-17.64/N-3.24/M}
0.4346=Q/(2512*N.^0.5*M.^0.5)*exp{-18.49/N-2.25/M}
令 x = Q/(2512*N.^0.5*M.^0.5),则有:
xe^(-16.81/N-3.0625/M) = 0.5325,-16.81/N-3.0625/M = ln0.5325 - lnx;①
xe^(-17.64/N-3.24/M) = 0.4947,-17.64/N-3.24/M = ln0.4947 - lnx;②
xe^(-18.49/N-2.25/M) = 0.4346,-18.49/N-2.25/M = ln0.4346 - lnx;③
① - ②,0.83/N - 0.1775/M = ln( 0.5325/0.4947);④
① - ③,1.68/N + 0.8125/M = ln( 0.5325/0.4346);⑤
⑤ * 0.83 - ④ * 1.68, 0.376175/M = 0.83ln( 0.5325/0.4346) - 1.68ln( 0.5325/0.4947)
M = 0.376175/[0.83ln( 0.5325/0.4346) - 1.68ln( 0.5325/0.4947)] = 8.374434422643842381;
代入4,0.83/N = ln( 0.5325/0.4947) + 0.1775/M = 0.224352291,
N = 0.83/0.224352291 = 3.6995387762234;
lnx = ln0.5325 +16.81/N + 3.0625/M = 4.27933360863541;
x = e^4.27933360863541 = 72.192315638543058832121;
Q = (2512*N.^0.5*M.^0.5)x = 1009397.3 。
这个需要私聊
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