设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于

设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于
设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于

设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于
m²+n²=7mn;
(m+n)²=7mn+2mn=9mn;
∴m+n=3√mn;
(m-n)²=7mn-2mn=5mn;
∴m-n=√5mn
(m²-n²)÷mn
=3√5mn÷mn
=3√5;
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(m²-n²)÷mn=t (m²-n²)=tmn 与原审联立得 m²=7+t/2*mn n²=7-t/2*mn
m²n²=49-t²/4m²n²
t=根号45=3*根号5