If d2 + 1/d2 = 18, and d > 1/d , then the value of d3 - 1/d3 is:

Explanation

Given: d2 + (1/d2) = 18, and d > 1/d Concept Used: We need to find the value of d3 - (1/d3) Calculation: Given d2 + (1/d2) = 18 Let x = d + (1/d) Then, x2 = d2 + 2 + (1/d2) → x2 = 18 + 2 = 20 → x = √20 = 2√5 We need to find d3 - (1/d3) We know that (d - (1/d))3 = d3 - (1/d3) - 3(d - (1/d)) Let y = d - (1/d) Then, y = √(x2 - 4) → y = √(20 - 4) = √16 = 4 Now, (d - (1/d))3 = d3 - (1/d3) - 3(d - (1/d)) → 43 = d3 - (1/d3) - 3 × 4 → 64 = d3 - (1/d3) - 12 → d3 - (1/d3) = 64 + 12 = 76 ∴ The value of d3 - (1/d3) is 76.