2023 · Q39
If x = (√3+1)/(√3-1) and y = (√3-1)/(√3+1) then what is the value x³ - y³?
Elementary MathematicsAlgebra
- A60
- B45√3
- C30√3
- D90
Explanation
Rationalising gives x = (√3+1)²/2 = 2 + √3 and y = (√3−1)²/2 = 2 − √3. Thus x − y = 2√3 and xy = 1. Using x³ − y³ = (x − y)³ + 3xy(x − y) yields (2√3)³ + 3(2√3) = 24√3 + 6√3 = 30√3 (C).