2021 · Q12
If α + β + γ = αβ + βγ + γα, then what is (1 − α)(1 − β)(1 − γ) equal to ?
Elementary MathematicsAlgebra
- A1 − αβγ
- B1 + αβγ
- Cα² + β² + γ²
- D(α − β)(β − γ)(γ − α)
Explanation
Expanding, (1 − α)(1 − β)(1 − γ) = 1 − (α+β+γ) + (αβ+βγ+γα) − αβγ. The given condition α+β+γ = αβ+βγ+γα makes the middle two terms cancel. The expression therefore equals 1 − αβγ. This is option (a).