Question

x² + 4y² + 9z² - 4xy + 12 yz - 6zx
please explain Step by step please for 50 points..​

Answer 1

Answer:

6:3:2

Step-by-step explanation:

x^2+4y^2+9z^2–2xy-6yz-3xz=0

or x^2–2xy+4y^2–6yz+9z^2–3xz=0

or x(x-2y)+2y(2y-3z)+3z(3z-x)=0

Therefore x-2y=0

x=2y or x/2=y/1=k(let)

x=2k , y=k ,

2y-3z=0 put y=k

2k-3z=0 or z=(2/3)k

Now x : y : z = 2k : k : 2k /3

x : y : z = 2 : 1 : 2/3

x : y : z =2×3 : 1×3 : ( 2/3)×3

x : y : z = 6 : 3 : 2 . , Answer

Answer 2

Step-by-step 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