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saintegg
@saintegg
July 2022
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Приведите квадратичную форму x²+7y²+4z²-4xy+6yz к каноническому виду методом лагранжа
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IrkaShevko
Verified answer
X² - 4xy + 7y² + 4z² + 6yz = (x² - 4xy + 4y²) - 4y² + 7y² + 4z² + 6yz =
= (x - 2y)² + 3y² + 6yz + 4z² = (x-2y)² + 3(y² + 2yz + z²) - 3z² + 4z² =
= (x - 2y)² + 3(y + z)² + z²
x₁ = x - 2y
x₂ = y + z
x₃ = z
Канонический вид:
x₁² + 3x₂² + x₃²
2 votes
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Answers & Comments
Verified answer
X² - 4xy + 7y² + 4z² + 6yz = (x² - 4xy + 4y²) - 4y² + 7y² + 4z² + 6yz == (x - 2y)² + 3y² + 6yz + 4z² = (x-2y)² + 3(y² + 2yz + z²) - 3z² + 4z² =
= (x - 2y)² + 3(y + z)² + z²
x₁ = x - 2y
x₂ = y + z
x₃ = z
Канонический вид:
x₁² + 3x₂² + x₃²