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Ответ:

14

Пошаговое объяснение:

((a-1) + 1/(a-1))² = 4²

(a-1)² + 1/(a-1)² + 2(a-1)/(a-1) = 16

(a-1)² + 1/(a-1)² + 2 = 16

(a-1)² + 1/(a-1)² = 14

Если a + 1/(a - 1) = 5, тогда

(a - 1) + 1/(a - 1) = 4.

Соответственно, (a - 1)^2 + 1/(a - 1)^2 = ((a - 1) + 1/(a - 1))^2 - 2•(a - 1) • 1/(a - 1) = ((a - 1) + 1/(a - 1))^2 - 2 = 4^2 - 2 = 16 - 2 = 14