If x-y-z - R then find Determinant 2x - 2 - x2 2x - 2 - x2 1 3x - 3 - x2 3x - 3 - x2 1 4x - 4 - x2 4x - 4 - x2 1

[ (2^x+2^ x)^2 amp;(2^x 2^ x)^2 amp;1; (3^x+3^ x)^2 amp;(3^x 3^ x)^2 amp;1; (4^x+4^ x)^2 amp;(4^x 4^ x)^2 amp; ...

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Definition of a Determinant

If x,y,z ∈ ...

Question

If $x, y, z \in R$ then find Determinant
$⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} {(2^{x} + 2^{- x})}^{2} & {(2^{x} - 2^{- x})}^{2} & 1 {(3^{x} + 3^{- x})}^{2} & {(3^{x} - 3^{- x})}^{2} & 1 {(4^{x} + 4^{- x})}^{2} & {(4^{x} - 4^{- x})}^{2} & 1 \end{matrix} ⎞ ⎟ ⎟ ⎟ ⎠$

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\frac{2 - x}{3} = \frac{2 y - 3}{3 k} = \frac{z - 4}{2}

\frac{2 - 2 x}{5 k} = \frac{y + 4}{2} = \frac{5 - z}{4}

k

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & x^{2} & x^{3} - 1 y & y^{2} & y^{3} - 1 z & z^{2} & z^{3} - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

x, y, z

4 + x y z

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