若m^2+n^2=4mn,求(m^2-n^2)/mn的值.

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若m^2+n^2=4mn,求(m^2-n^2)/mn的值.若m^2+n^2=4mn,求(m^2-n^2)/mn的值.若m^2+n^2=4mn,求(m^2-n^2)/mn的值.答：m^2+n^2=4mn

若m^2+n^2=4mn,求(m^2-n^2)/mn的值.
若m^2+n^2=4mn,求(m^2-n^2)/mn的值.

若m^2+n^2=4mn,求(m^2-n^2)/mn的值.
答：
m^2+n^2=4mn>=0
所以：
(m+n)^2=6mn
(m-n)^2=2mn
两式相乘得：
(m^2-n^2)^2=12(mn)^2
所以：m^2-n^2=±(2√3)mn
所以：
(m^2-n^2)/(mn)=±2√3

∵m^2+n^2=4mn
m^2-2mn+n^2=2mn
(m-n)^2=2mn
∴m-n=±√(2mn)
∵m^2+n^2=4mn
m^2+2mn+n^2=6mn
(m+n)^2=6mn
∴m+n=±√(6mn)
则(m^2-n^2)/mn=(m+n)(m-n)/mn
=±√(2mn)√(6mn)/mn
=±√12
=±2√3

两边同除mn得(m/n)+（n/m)=4令m/n=X即x+1/x=4
(m^2-n^2)/mn将n^2=4mn-m^2带入得
2m/n-4
即2x-4=2(x-2)
x-1/x=4化简为x^2-4x=1 即（x-2）^2=3
解得x-2=正负根号3
则为正负2*3^（1/2）-4

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