If a,b,c are all distinct and `|[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|` =0, show that abc(ab+bc+ac) = a+b+c

Answer

Proved

Explanation

ATQ,
$$
\left|\begin{array}{lll}
a & a^{3} & a^{4} \\
b & b^{3} & b^{4} \\
c & c^{3} & c^{4}
\end{array}\right|-\left|\begin{array}{lll}
a & a^{3} & 1 \\
...