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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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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