论文部分内容阅读
1995年河北省唐山市初中数学竞赛试卷中有一道题,是证明下面的拉格朗日恒等式:(a~2+b~2+c~2)(m~2+n~2+k~2)-(am+bn+ck)~2=(an-bm)~2+(bk-cn)~2+(cm-ak)~2.把恒等式左右两边分别展开、合并,易知恒等式成立.
There was a question in the 1995 Tangshan Middle School Mathematics Contest Test Paper in Hebei proving the following Lagrange identities: (a ~ 2 + b ~ 2 + c ~ 2) (m ~ 2 + n ~ 2 + k ~ 2 ) - (am + bn + ck) ~ 2 = (an-bm) ~ 2 + (bk-cn) ~ 2 + (cm-ak) ~ 2. Expand the identities on the left and right sides and merge them.