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The Transform inverse Z for resolve
(2z²-7z+7)/((z-1)²(z-2))"

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Final answer:

The student's question pertains to finding the inverse Z-transform of a given rational function. The method required for resolution is partial fraction decomposition followed by applying standard Z-transform pairs or integral definitions.

Step-by-step explanation:

The question involves finding the inverse Z-transform of the function F(z) = (2z² - 7z + 7)/((z - 1)²(z - 2)). To find the inverse Z-transform, one approach is to decompose the function into simpler fractions that can be individually inverted. This process is known as partial fraction decomposition. After decomposition, the inverse Z-transform can be found using standard Z-transform pairs or by applying the definition of the inverse Z-transform through contour integration in the complex plane.

To carry out partial fraction decomposition, we would express F(z) as a sum of terms of the form A/(z - a), B/(z - b), etc., where A, B, etc., are coefficients to be determined and a, b, etc., are poles of the original function. Once the coefficients are found, the inverse Z-transform can be directly obtained by referring to standard tables or using known properties.

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