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The difference between a fraction and its reciprocal is 9/11. If the cubes of both the fraction and its reciprocal are considered, then what will be the difference between them?

The difference between a fraction and its reciprocal is 9/11. If the cubes of both the fraction and its reciprocal are considered, then what will be the difference between them? Correct Answer 3996/1331

Let the fraction be x/y, then its reciprocal will be y/x.

According to the question,

x/y – y/x = 9/11

Cubing on both sides,

(x/y – y/x)3 = (9/11)3

(x/y)3 – (y/x)3 – 3 (x/y – y/x) = 729/1331

(x/y)3 – (y/x)3 – 3 × 9/11 = 729/1331

(x/y)3 – (y/x)3 – 3 × 9/11 = 729/1331

(x/y)3 – (y/x)3 = 729/1331 + 3 × 9/11

(x/y)3 – (y/x)3 = 729/1331 + 27/11

(x/y)3 – (y/x)3 = (729 + 27 × 121)/1331

(x/y)3 – (y/x)3 = (729 + 3267)/1331

(x/y)3 – (y/x)3 = 3996/1331

Thus, the correct answer is option 1.

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