2022 · Q3
If (a³ + b³) is proportional to (a² - b²), then (a² - ab + b²) is proportional to
Elementary MathematicsRatio and Proportion
- A(a - b)
- B(a + b)
- C(a + ab + b)
- D(a3 - b3)
Explanation
Factor a³+b³ = (a+b)(a²−ab+b²) and a²−b² = (a+b)(a−b). The hypothesis says (a+b)(a²−ab+b²) = k(a+b)(a−b) for some constant k; cancelling (a+b) gives a²−ab+b² = k(a−b). Hence (a²−ab+b²) is proportional to (a−b). The keyed option is A.