Let $a, b, c$ be three positive real numbers. The value of the determinant $ \ \left|\begin{array}{

Question

Let $a, b, c$ be three positive real numbers. The value of the determinant $ \ \left|\begin{array}{ccc} \sqrt{a}+\sqrt{b} & 2 \sqrt{c} & \sqrt{c} \ \sqrt{b c}+\sqrt{2 a} & c & \sqrt{2 c} \ b+\sqrt{a c} & \sqrt{b c} & c \end{array}ight| 	ext { is } $

Professor PC Thomas Classes · Answer

Iterative row simplification targets structural zeroes enforcing polynomial simplifications explicitly yielding choice 1.