用公式法解下列一元二次方程,

(m²-n²)x² -4mnx =m²-n²即
(m²-n²)x² -4mnx -(m²-n²)=0
由公式得到
x= {4mn+√[16m²n²+4(m²-n²)²] } / 2(m²-n²)
或 {4mn -√[16m²n²+4(m²-n²)²] } / 2(m²-n²)
而
√[16m²n²+4(m²-n²)²]
=√[4(m²+n²)²]
=2(m²+n²)
所以
x=(4mn+2m²+2n²)/2(m²-n²)=(m+n)²/(m²-n²)= (m+n)/(m-n)
或(4mn-2m²-2n²)/2(m²-n²)= -(m-n)²/(m²-n²)= (n-m)/(m+n)
解得
x=(m+n)/(m-n)或 (n-m)/(m+n)