Question

If a b c=0, but abc don't equal 0, then a^2/bc b^2/ca c^2/ab=

Answer 1

`\sf a + b + c = 0\\abc \\eq 0\\\\ (a^2)/(bc) + (b^2)/(ac) + (c^2)/(ab) = (a^3+b^3+c^3)/(abc) \\\\\sf Formula: \\a^3 + b^3 + c^3 = (a + b + c) (a^2 + b^2 + c^2- ab - bc - ca) + 3abc\\\\(a^3+b^3+c^3)/(abc)= ((a + b + c) (a^2 + b^2 + c^2- ab - bc - ca) + 3abc)/(abc)\\\\\sf However, ~a+b+c = 0. ~So:\\\\(0 (a^2 + b^2 + c^2- ab - bc - ca) + 3abc)/(abc)\\\\\sf Multiply~ anything ~by~ 0, ~and~ you ~get~ 0. ~So~ simplifying:\\\\(3abc)/(abc) = \boxed{3}`

Your final answer is 3.