Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average age of Paolo, Qing and Rayna is 13. Determine their ages. Prove that, for all integers K and L, there is at least one pair of integers (a, b) for which K2 + 3L2 = a2 + b2 − ab.Prove that, for all integers a and b, there is at least one pair of integers (K, L) for which K2 + 3L2 = a2 + b2 − ab.

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 51E

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Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average age of Paolo, Qing and Rayna is 13. Determine their ages.
Prove that, for all integers K and L, there is at least one pair of integers (a, b) for which K² + 3L² = a² + b² − ab.
Prove that, for all integers a and b, there is at least one pair of integers (K, L) for which K² + 3L² = a² + b² − ab.

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