设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于

题目

设m大于n大于0,m²+n²=7mn,则(m²-n²)÷mn的值等于

答案

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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