If x > 1 and x2 + = 83, then x3 − is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 756.
x2 + 1/x2 = 83
⇒ (x - 1/x)2 + 2 = 83
⇒ (x - 1/x)2 = 83 - 2 = 81
⇒ (x - 1/x) = √81 = 9
If x - (1/x) = a then x3 - 1/x3 = a3 + 3a
So, x3 - 1/x3 = 93 + (3 × 9) = 729 + 27 = 756
Therefore, the value of the expression is 756.