If a, b, c > 0 & x, y, z ∈ R then the determinant | array ccc (a^ x +a^ -x )^ 2 & (a^ x…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If a, b, c > 0 & x, y, z ∈ R then the determinant
\[\left|\begin{array}{ccc} \left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{y}+b^{-y}\right)^{2} & \left(b^{y}-b^{-y}\right)^{2} & 1 \\ \left(c^{z}+c^{-z}\right)^{2} & \left(c^{z}-c^{-z}\right)^{2} & 1 \end{array}\right|=\]
\[\left|\begin{array}{ccc} \left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{y}+b^{-y}\right)^{2} & \left(b^{y}-b^{-y}\right)^{2} & 1 \\ \left(c^{z}+c^{-z}\right)^{2} & \left(c^{z}-c^{-z}\right)^{2} & 1 \end{array}\right|=\]
- ax by cz
- a–x b–y c–z
- a2x b2y c2z
- zero
Answer
(D) zero
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