2019 · Q12
If x = (1 + √3)/2 and y = x³, then y satisfies which one of the following equations?
Elementary MathematicsAlgebra
- A8y² - 20y - 1 = 0
- B8y² + 20y - 1 = 0
- C8y² + 20y + 1 = 0
- D8y² - 20y + 1 = 0
Explanation
x = (1+sqrt(3))/2 gives 2x-1 = sqrt(3), i.e. 2x^2-2x-1 = 0. Cubing, y = x^3 = (3x+1)/2, so x = (2y-1)/3. Substituting in 2x^2-2x-1 = 0 and multiplying by 9: 2(2y-1)^2-6(2y-1)-9 = 0, which simplifies to 8y^2-20y-1 = 0.