Q.Factorise :-
i) x2 + 4y2 + 9z2 - 4xy -12yz + 6xz
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x2 + 4y2 + 9z2 - 4xy -12yz + 6xz
4x² + y² + 9z² - 2xy - 3yz - 6zx = 0
Multiply by 2
=> 8x² + 2y² + 18z² - 4xy - 6yz - 12zx = 0
=> 4x² + 4x² + y² + y² + + 9z² + 9z² + - 4xy - 6yz - 12zx = 0
=> 4x²+ y² - 4xy + 4x² + 9z² - 12xz + y² + 9z² - 6yz = 0
=> (2x - y)² + (2x -3z)² + (y - 3z)² = 0
Square can not be - ve
& sum = 0
=> (2x - y)² = 0 => 2x = y
(2x -3z)² = 0 => 2x = 3z
(y - 3z)² = 0 => y = 3z
Hence 2x = y = 3z.
Step-by-step explanation:
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