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provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 22

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Answer: zero

Hint: Here, we use basic concept of determinant of matrix

Given:  \left[\begin{array}{lll} \left(2^{x}+2^{-x}\right)^{2} & \left(2^{x}+2^{-x}\right)^{2} & 1 \\ \left(3^{x}+3^{-x}\right)^{2} & \left(3^{x}+3^{-x}\right)^{2} & 1 \\ \left(4^{x}+4^{-x}\right)^{2} & \left(4^{x}+4^{-x}\right)^{2} & 1 \end{array}\right]

Solution:  Here, clearly 2 column has same value

                According to property of determinant, if two column has same value then determinant of matrix should be zero.

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