2014 · Q17
If (x^2 + 1/x^2) = 17/4, then what is (x^3 - 1/x^3) equal to?
Elementary MathematicsAlgebra
- A75/16
- B63/8
- C95/8
- DNone of the above
Explanation
(x - 1/x)^2 = 17/4 - 2 = 9/4, so x - 1/x = 3/2; then x^3 - 1/x^3 = (3/2)^3 + 3(3/2) = 63/8.
If (x^2 + 1/x^2) = 17/4, then what is (x^3 - 1/x^3) equal to?
Explanation
(x - 1/x)^2 = 17/4 - 2 = 9/4, so x - 1/x = 3/2; then x^3 - 1/x^3 = (3/2)^3 + 3(3/2) = 63/8.