SOLUTION: if {{{a/b=b/c=c/d}}}, then prove that {{{(a^3+b^3+c^3)/(b^3+c^3+d^3)}}}{{{""=""}}}{{{a/d}}}

Algebra ->  Finance -> SOLUTION: if {{{a/b=b/c=c/d}}}, then prove that {{{(a^3+b^3+c^3)/(b^3+c^3+d^3)}}}{{{""=""}}}{{{a/d}}}      Log On


   



Question 1188899: if a%2Fb=b%2Fc=c%2Fd, then prove that %28a%5E3%2Bb%5E3%2Bc%5E3%29%2F%28b%5E3%2Bc%5E3%2Bd%5E3%29%22%22=%22%22a%2Fd
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
if a%2Fb=b%2Fc=c%2Fd, then prove that %28a%5E3%2Bb%5E3%2Bc%5E3%29%2F%28b%5E3%2Bc%5E3%2Bd%5E3%29%22%22=%22%22a%2Fd
Let k=a%2Fb=b%2Fc=c%2Fd, then

matrix%281%2C5%2Ca=kb%2C+%22%2C%22%2C+b=kc%2C%22%2C%22%2C+c=kd%29

a=k%28kc%29=k%5E2c=k%5E2%28kd%29=k%5E3d

b=kc=k%28kd%29=k%5E2d

So, since a=k%5E3d, b=k%5E2d, and c=kd,

%28a%5E3%2Bb%5E3%2Bc%5E3%29%2F%28b%5E3%2Bc%5E3%2Bd%5E3%29%22%22=%22%22%22%22=%22%22

%28k%5E9d%5E3%2Bk%5E6d%5E3%2Bk%5E3d%5E3%29%2F%28k%5E6d%5E3%2Bk%5E3d%5E3%2Bd%5E3%29%22%22=%22%22%28k%5E3d%5E3%28k%5E6%2Bk%5E3%2B1%29%29%2F%28d%5E3%28k%5E6%2Bk%5E3%2B1%29%29%22%22=%22%22
%22%22=%22%22k%5E3

Since a=k%5E3d, k%5E3=a%2Fd, so

%28a%5E3%2Bb%5E3%2Bc%5E3%29%2F%28b%5E3%2Bc%5E3%2Bd%5E3%29%22%22=%22%22a%2Fd

Edwin