# Homework Help: Ratio proportion problem

1. Jan 17, 2012

### 1/2"

1. The problem statement, all variables and given/known data
if(i have attached the equation's pic) then
prove a=b=c or (a+b+c)(x+y+z)=ax+by+cz

2. Relevant equations
if a/b=c/d=e/f
each ratio = (a+c+e)/(b+d+f)

3. The attempt at a solution
I was able to prove (a+b+c)(x+y+z)=ax+by+cz
like this:
each ratio= (a2+b2+c2-ab-bc-ca)/x+y+z
also
each ratio= (a3+b3+c[SUP3[/SUP]-3abc)/ax+by+cz
(i hope i could make you understand how i did this)
since
(a2+b2+c2-ab-bc-ca)/x+y+z =(a3+b3+c[SUP3[/SUP]-3abc)/ax+by+cz
→(a2+b2+c2-ab-bc-ca)/x+y+z=
(a+b+c)(a2+b2+c2-ab-bc-ca)/ax+by+cz
therefore
(a+b+c)(x+y+z)=ax+by+cz
fine uptill here but i can't understand how do i prove a=b=c??
tried it like this
(a+b+c)(x+y+z)=ax+by+cz
→bx+cx+ay+cy+az+bz=0

i can go further than this .Please give me a clue .
And if i have gone wrong somewhere please point it out.
Thank you.

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Last edited: Jan 17, 2012
2. Jan 17, 2012

### SammyS

Staff Emeritus
No picture is attached.

3. Jan 18, 2012

### HallsofIvy

Well, the picture is attached but there is no equation in it- just a sum of three expressions. What was this supposed to be equal to?