If x2 + 4y2 + 9z2 – 4xy – 12yz + 6xz = 0, then
(1) x = 2y – 3z
(2) x = y – 3z
(3) 2x = y – 3z
(4) x = 3y – 2z
Correct option: (1) x = 2y – 3z
Explanation:
x2 + 4y2 + 9z2 – 4xy – 12yz + 6xyz = 0
(x)2 + (–2y)2 + (3z)2 + 2xy(–2y) + 2(–2y) 3z + 2 × x × 3z
(x – 2y + 3z)2 = 0
x – 2y + 3z = 0 ⇒ x = 2y – 3z
