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.