1. The problem statement, all variables and given/known data If a,b,c are real numbers satisfying the equation [itex]25(9a^2+b^2)+9c^2-15(5ab+bc+3ca)=0[/itex], then prove that a,b,c are in A.P. 2. Relevant equations 3. The attempt at a solution Rearranging the question I can say that I have to prove this 2b=a+c I tried simplifying the terms and I arrived at this [itex](15a+5b+3c)^2=45(5ab+bc+3ac)[/itex] Any ideas how should I proceed?