A Vanishing Determinant

★ 6/10algebra Linear Algebra Polynomials

Problem

Let $a, b, c, d$ be real numbers with $abcd = 1$ . Prove that

\begin{vmatrix} a^2 + \dfrac{1}{a^2} & a & \dfrac{1}{a} & 1 \\[2pt] b^2 + \dfrac{1}{b^2} & b & \dfrac{1}{b} & 1 \\[2pt] c^2 + \dfrac{1}{c^2} & c & \dfrac{1}{c} & 1 \\[2pt] d^2 + \dfrac{1}{d^2} & d & \dfrac{1}{d} & 1 \end{vmatrix} = 0.

Answer

Solution

Difficulty	6/10
Topics	algebra, Linear Algebra, Polynomials

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