2014 · Q34
If ax + by − 2 = 0 and axby = 1, where a ≠ 0, b ≠ 0, then what is (a²x + b²y) equal to?
Elementary MathematicsAlgebra
- Aa + b
- B2ab
- Ca³ + b³
- Da⁴ + b⁴
Explanation
Put u = ax, v = by: u + v = 2, uv = 1, so u = v = 1, i.e. x = 1/a, y = 1/b. Then a²x + b²y = a + b.