Question

1.) If 4x2 + y2 + 9z2 - 2xy - 3yz - 6zx = 0, then prove that 2x = y = 3z.
Evaluate :
2.) 7/2² - 623 +7(62_c23 +7(02-223
(a - b) + (6 - C)® +(c-a)

3.) If V2x + V3y = 15. prove that
212x3 +3/3y3 - 5/5 + 330xy = 0

Please solve fast I'm in hurry!!​

Answer 1

Answer:

2x = y = 3z

Step-by-step explanation:

If 4x2 + y2 + 9z2 - 2xy - 3yz - 6zx = 0, then prove that 2x = y = 3z.

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.

Answer 2

Step-by-step explanation:

2x=y=3z

hence proved

I hope it will help you