SOLUTION: a/b=c/d=e/f, a^3+c^3+e^3/b^3+d^3+f^3=?

Algebra.Com
Question 1086326: a/b=c/d=e/f, a^3+c^3+e^3/b^3+d^3+f^3=?
Found 2 solutions by AnlytcPhil, ikleyn:
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
 let each of those equal to k. Then

, , 











So 



Edwin


Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

From Wikipedia article https://en.wikipedia.org/wiki/Lemma_(mathematics)
    In mathematics, a  lemma (a "helping theorem") is a proved proposition which is used as a stepping stone 
    to a larger result rather than as a statement of interest by itself. 

Lemma 1.  

    If  =  then  =  = .


        Proof. Let  =  = k. Then

               a = b*k,  c = d*k  and   =  =  = k =  = .

        The lemma is proved.



Lemma 2. 

    If  =  =   then   =  = .


       The proof is obvious.



Major statement.   = .


    Proof. It follows IMMEDIATELY Lemma 1  and  Lemma 2.



RELATED QUESTIONS

A=3; B=13 G-A=3 F+G=D C+D+E=B C-D=G B+E=C+D Please solve this for... (answered by checkley71)
How many subsets of 3 elements does the set (a, b, c, d, e, f)... (answered by robertb)
How many 3-element subsets does the set (A, B, C, D, E, F)... (answered by ikleyn)
Given f(x)=3x - 1, find a. f(2) b. f(-1) c. f(0) d. f(2/3) e. f(k) f. f(k +... (answered by checkley77)
Given f(x)=3x - 1, find a. f(2) b. f(-1) c. f(0) d. f(2/3) e. f(k) f.... (answered by rfer)
Let U={a, b, c, d, e, f, 1, 2, 3, 4, 5, 9} A={a, b, c, 1, 3, f} B={5, e, f, 3} find Ac... (answered by greenestamps)
The function f(x) is symmetric with respect to the origin. If f(2)=-3, then f(−2)= (answered by Edwin McCravy)
The function f(x) is symmetric with respect to the origin. If f(2)=-3, then f(-2)=... (answered by Edwin McCravy)
1. ~(~C • D) 2. ~D ⊃ E 3. C ⊃ ~F //F ⊃ E (answered by Edwin McCravy)