Question

已知x/a+y/b+z/c=1,a/x+b/y+c/z=0,求x2/a2+y2/b2+z2/c2的值

Answer 1

令x/a=m,y/b=n,z/c=p

m+n+p=1,1/m+1/n+1/p=0,求m^2+n^2+p^2的值.

1/m+1/n+1/p=0,mn+np+mp=0

(m+n+p)^2=m^2+n^2+p^2+2(mn+np+mp)=m^2+n^2+p^2=1

所以：m^2+n^2+p^2=1,即所求的值是1.