已知a/m=b/n=c/p 求证（aa+bb+cc)=(am+bn+cp)*(am+bn+cp)

设a/m=b/n=c/p=k,a=km.b=kn,c=kp (a^2+b^2+c^2)(m^2+n^2+p^2) =[(km)^2+(kn)^2+(kp)^2](m^2+n^2+p^2) =k^2(m^2+n^2+p^2)^2 =[k(m^2+n^2+p^2)]^2 =(km*m+kn*n+kp*p)^2 =(am+bn+cp)^2