2016 · Q6
If x = 2^(1/3) + 2^(−1/3), then the value of 2x³ − 6x − 5 is equal to
Elementary MathematicsAlgebra
- A0
- B1
- C2
- D3
Explanation
Cubing with (a+b)³ = a³+b³+3ab(a+b): x³ = 2 + 2⁻¹ + 3·2^{1/3}·2^{−1/3}·x = 5/2 + 3x. Then 2x³−6x−5 = 2(5/2+3x)−6x−5 = 5+6x−6x−5 = 0. Hence the value is 0, option A.