2021 · Q23
What is x⁴/((x² − y²)(x² − z²)) + y⁴/((y² − x²)(y² − z²)) + z⁴/((z² − x²)(z² − y²)) equal to ?
Elementary MathematicsAlgebra
- A−1
- B0
- C1
- Dx² + y² + z²
Explanation
This is a standard cyclic identity: bringing the three fractions to the common denominator (x²−y²)(y²−z²)(z²−x²), the numerator simplifies to exactly that denominator. The sum therefore equals 1 for all distinct x, y, z (verified numerically, e.g. at (2,3,5)). This is option (c).