已知x/a+y/b+z/c=1a/x+y/b+c/z=0求xx/aa+yy/bb+zz/cc的值

Question

已知x/a+y/b+z/c=1 a/x+y/b+c/z=0 求xx/aa+yy/bb+zz/cc的值

Answer 1

设m=x/a,n=y/b,p=z/c由已知可得：m+n+p=1,1/m+1/n+1/p=0通分可得：pn+mp+mn=0要求的=m^2+n^2+p^2=（m+n+p）^2-2(pn+mp+mn)=1