设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值

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设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值

设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值
设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值

设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值
m^2+n^2=4mn
所以m²+n²+2mn=6mn,m²+n²-2mn=2mn
即(m+n)²=6mn,(m-n)²=2mn
因为m>n>0
所以m+n=√(6mn),m-n=√(2mn)
故(m²-n²)/mn
=(m+n)(m-n)/mn
=√(6mn)x√(2mn)/mn
=√12mn/mn
=√12
=2√3