已知1/M-1/N=5,NM=-1,求1/M^4+1/N^4的值

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已知1/M-1/N=5,NM=-1,求1/M^4+1/N^4的值
已知1/M-1/N=5,NM=-1,求1/M^4+1/N^4的值

已知1/M-1/N=5,NM=-1,求1/M^4+1/N^4的值
N-M/MN=5
N-M=-5
1/M^4+1/N^4=(1/M^2+1/N^2)^2-2*1/M^2*N^2=(1/M^2+1/N^2)^2-2
=(N^2+M^2/M^2*N^2)^2-2=527

531

通分的：n-m=-5
mn=-1
然后就可以求出(m+n)^2=(m-n)^2+4*mn=25-4=21,
n+m=21^1/2
这样就可以求了

n-m=5mn=5
(1/m+1/n)^4=1/m^4+1/n^4+4/mn-(4/m^3n+4/mn^3)+2/m^2n^2
=1/m^4+1/n^4-4-[(4m^2+4n^2)/m^3n^3]+2
=1/m^4+1/n^4-2+4(m^2+n^2)
m^2+n^2=25-2=23
1/m^4+1/n^4-2+4(m^2+n^2)
=1/m^4+...

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n-m=5mn=5
(1/m+1/n)^4=1/m^4+1/n^4+4/mn-(4/m^3n+4/mn^3)+2/m^2n^2
=1/m^4+1/n^4-4-[(4m^2+4n^2)/m^3n^3]+2
=1/m^4+1/n^4-2+4(m^2+n^2)
m^2+n^2=25-2=23
1/m^4+1/n^4-2+4(m^2+n^2)
=1/m^4+1/n^4+90
(1/m-1/n)^2=25
1/m^2+1/n^2=25-2=23
(1/m+1/n)^2=23-2=21
(1/m+1/n)^4=441
1/m^4+1/n^4+90=(1/m+1/n)^4
1/m^4+1/n^4=441-90=351

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