Find $abc$ where $a^2+b^2+c^2=144$ and $ab+bc+ca=144$ Total surface area of a cuboid is 288 sq.cm. and length of a diagonal of it is 12 cm. Find its volume.
This is the question. We know that diagonal =$a^2+b^2+c^2$ and surface area =$2(ab+bc+ca)$ and volume =$abc$ . So finally we have to find the value of $abc$ where $$a^2+b^2+c^2=144$$ and $$ ab+bc+ca =144 .$$ Somebody please help me.

Hint:
$$a^2+b^2+c^2=ab+bc+cc \Leftrightarrow a=b=c \Leftrightarrow (a-b)^2+(b-c)^2+(c-a)^2=0$$
