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max x² + y² subject to: a² + xy + y² = 3

max x² + y² subject to: a² + xy + y² = 3

Advanced Engineering Mathematics
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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Solution: Next, solve the system or max 2² +² subject to: x² + xy + y² = 3 L(x, y, A) = (x² + y²) + (x² + xy + y² − 3) Ə :((x² + y²) + λ (x² + xy + y² − 3)) = A (2x+y)+2x ?х : ((x² + y²) + λ (x² + xy + y² − 3)) = A (x + 2y) + 2y · ((x² + y²) + λ (x² + xy + y² − 3)) = x² + xy + −3 远古西征 |||||| = 0 A (2x+y)+2x = 0 X(x+2y)+2y=0 [x² + xy + y² − 3=0 The system has the following real solutions: (x, y, X) = (-1,-1, -2/3), (x, y, A) = (1, 1, -2/3), (x, y, X) = (-√3, √3, -2) (x, y, X) = (√³3, -√3, -2)
Transcribed Image Text:Solution: Next, solve the system or max 2² +² subject to: x² + xy + y² = 3 L(x, y, A) = (x² + y²) + (x² + xy + y² − 3) Ə :((x² + y²) + λ (x² + xy + y² − 3)) = A (2x+y)+2x ?х : ((x² + y²) + λ (x² + xy + y² − 3)) = A (x + 2y) + 2y · ((x² + y²) + λ (x² + xy + y² − 3)) = x² + xy + −3 远古西征 |||||| = 0 A (2x+y)+2x = 0 X(x+2y)+2y=0 [x² + xy + y² − 3=0 The system has the following real solutions: (x, y, X) = (-1,-1, -2/3), (x, y, A) = (1, 1, -2/3), (x, y, X) = (-√3, √3, -2) (x, y, X) = (√³3, -√3, -2)
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