+58 Non-negative real numbers $a, b,$ and $c$ satisfy $$a^2+b^2+c^2+70=35ab+7ac+5bc.$$ The least possible value of $a^2+2b^2+3c^2$ can be expressed as $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. FInd $m+n.$
So I don't really know how to start on this problem, all I noticed that you can use the factorization $(a+b+c)^2=a^2+b^2+c^2+2(ab+ac+bc),$ other than this, I don't really know how to do this problem. Any solutions and hints would be appreciated!
