14*(a^2+b^2+c^2)=(a+2b+3c)^214a^2+14b^2+14c^2=a^2+4b^2+9c^2+4ab+6ac+12bc13a^2+10b^2+5c^2=4ab+6ac+12bca=113+10b^2+5c^2=4b+6c+12bc(c-3)^2+(b-2)^2+(3b-2c)^2=0c=3b=2