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756Step-by-step explanation:we KNOW that, (X - 1/x)² = x² + (1/x)² - 2(x)(1/x)Given, x² + 1/x² = 83=> (x - 1/x)² = 83 - 2 = 81=> x - 1/x = √81 = 9cubing on both SIDES, (x - 1/x)³ = x³ - (1/x)³ - 3(x)(1/x)[x - 1/x]=> (9)³ = x³ - (1/x)³ - 3(9)=> 729 + 27 = x³ - 1/x³=> x³ - 1/x³ = 756



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