X² + 5y² - 4z² + 2xy - 4xz =
= (x² + 2xy - 4xz) + 5y² - 4z² =
= (x² + 2 * x * (y - 2z) + (y-2z)²) - (y-2z)² + 5y² - 4z² =
= (x + y - 2z)² - y² - 4z² + 4yz + 5y² - 4z² =
= (x + y - 2z)² + 4y² + 4yz - 8z² =
= (x + y - 2z)² + (4y² + 2 * 2y * z + z²) - z² - 8z² =
= (x + y - 2x)² + (2y + z)² - 9z²
x₁ = x + y - 2x
x₂ = 2y + z
x₃ = 3z
x₁² + x₂² - x₃² = 0 -канонический вид