If 4/3(x2 + (1/x2)) = 110 (2/3), find 1/9(x3 - (1/x3)), where x > 0.
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Correct answer: C
Explanation
The correct answer is option 3 i.e 84
⇒ (4/3)(x2 + (1/x2)) = 110(2/3)
⇒ (4/3){(x - 1/x)2 - 2} = 332/3
⇒ (x - 1/x)2 + 2= 83
⇒ (x - 1/x)2 = 81
⇒ x - 1/x = 9
⇒ (1/9){x3 - (1/x3)} = (1/9){(x - 1/x)3 + 3(x - 1/x)}
⇒ (1/9){(93 + 3 × 9} = (1/9)(729 + 27)
⇒ 81 + 3 = 84