设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于

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设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值

设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于
设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于

设m>n>0,m^2+n^2=4mn,则m^2-n^2/mn的值等于
(m+n)^2=m^2+n^2+2mn=4mn+2mn=6mn
(m-n)^2=m^2+n^2-2mn=4mn-2mn=2mn
(m^2-n^2)^2=(m+n)^2(m-n)^2=6mn*2mn=12m^2n^2
m^2-n^2=2√3mn
m^2-n^2/mn=2√3

(m+n)²=m²+n²+2mn=4mn+2mn=6mn
(m-n)²=m²+n²-2mn=4mn-2mn=2mn
(m²-n²)²=(m+n)²(m-n)²=6mn×2mn=12m²n²又∵m>n>0
∴m²-n²=2√3mn
∴(m²-n²)/mn=2√3

m^2+n^2=4mn得m/n+n/m=4 设m/n=x 则x+1/x=4 (x>1)
则(x-1/x)^2=(x+1/x)^2-4=16-4=12
故x-1/x=2√3
则m^2-n^2/mn=m/n-n/m=x-1/x=2√3