已知实数m,n,且m>n>0,m²+n²=4mn,则m²﹣n²/mn的值等于∵(m+n)²=m²+2mn+n²,(m-n)²=m²-2mn+n²,m²+n²=4mn.(m+n)²=6mn(m-n)²=2mn(m+n)²(m-n)²=12m²n²mm³-2m
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![已知实数m,n,且m>n>0,m²+n²=4mn,则m²﹣n²/mn的值等于∵(m+n)²=m²+2mn+n²,(m-n)²=m²-2mn+n²,m²+n²=4mn.(m+n)²=6mn(m-n)²=2mn(m+n)²(m-n)²=12m²n²mm³-2m](/uploads/image/z/129077-53-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0m%2Cn%2C%E4%B8%94m%3En%3E0%2Cm%26%23178%3B%2Bn%26%23178%3B%3D4mn%2C%E5%88%99m%26%23178%3B%EF%B9%A3n%26%23178%3B%2Fmn%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E%E2%88%B5%28m%2Bn%29%26%23178%3B%3Dm%26%23178%3B%2B2mn%2Bn%26%23178%3B%2C%28m-n%29%26%23178%3B%3Dm%26%23178%3B-2mn%2Bn%26%23178%3B%2Cm%26%23178%3B%2Bn%26%23178%3B%3D4mn.%28m%2Bn%29%26%23178%3B%3D6mn%28m-n%29%26%23178%3B%3D2mn%28m%2Bn%29%26%23178%3B%28m-n%29%26%23178%3B%3D12m%26%23178%3Bn%26%23178%3Bmm%26%23179%3B-2m%26%231)
已知实数m,n,且m>n>0,m²+n²=4mn,则m²﹣n²/mn的值等于∵(m+n)²=m²+2mn+n²,(m-n)²=m²-2mn+n²,m²+n²=4mn.(m+n)²=6mn(m-n)²=2mn(m+n)²(m-n)²=12m²n²mm³-2m
已知实数m,n,且m>n>0,m²+n²=4mn,则m²﹣n²/mn的值等于
∵(m+n)²=m²+2mn+n²,(m-n)²=m²-2mn+n²,
m²+n²=4mn.
(m+n)²=6mn
(m-n)²=2mn
(m+n)²(m-n)²=12m²n²
mm³-2m²n²+nn³=12m²n²
(m²-n²)²=12m²n²
m²-n²=2mn√3
∴m²-n²/mn=2√3
我知道了……
已知实数m,n,且m>n>0,m²+n²=4mn,则m²﹣n²/mn的值等于∵(m+n)²=m²+2mn+n²,(m-n)²=m²-2mn+n²,m²+n²=4mn.(m+n)²=6mn(m-n)²=2mn(m+n)²(m-n)²=12m²n²mm³-2m
你的做法很好,还可以这样做:假设m/n=t,要求的就是t-1/t的值,已知的就是t+1/t=4.
只要把t+1/t=4平方,则有t² + 1/t² +2 =16,所以t² + 1/t²=14
把t-1/t平方,则有t² + 1/t² -2=12.所以m²﹣n²/mn=t-1/t=√(12)=2√3
12
呵呵,还好啦