If 2x^2 + 3y^2 + 4z^2 - √6xy - 2√3yz-2√2xz = 0,
then find the value of
(2x^2 + 3y^2 +16z^² +2√6xy - 8√3y2- 8√2xz).
Answers
Answer:
2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz = 0
Step-by-step explanation:
If 2x^2 + 3y^2 + 4z^2 - √6xy - 2√3yz-2√2xz = 0,
then find the value of
(2x^2 + 3y^2 +16z^² +2√6xy - 8√3yz- 8√2xz).
2x² + 3y² + 4z² - √6xy - 2√3yz-2√2xz = 0
multiplying by 2
=> 4x² + 6y² + 8z² - 2√6xy - 4√3yz-4√2xz = 0
=> 4x² + 6y² + 8z² - 2√6xy - 4√3yz-4√2xz = 0
=> 2x² + 2x² + 3y² + 3y² + 4z² + 4z²- 2√6xy - 4√3yz-4√2xz = 0
=> 2x² + 3y²- 2√6xy + 2x² + 4z² + -4√2xz + 3y² + 4z² - 4√3yz = 0
=> ( √2x - √3y)² + (√2x - 2z)² + (√3y - 2z)² = 0
As square can not be negative
=> (√2x - √3y)² = (√2x - 2z)² = (√3y - 2z)² = 0
=> √2x = √3y , √2x = 2z , √3y = 2z
=> √2x = √3y = 2z
=> 2x² = 3y² = 4z²
2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz
Putting values of y & z in form of x
= 2x² + 2x² + 8x² + 2√2x√2x - 8√2x.x/√2 - 8√2x.x/√2
= 12x² + 4x² - 8x² - 8x²
= 16x² - 16x²
= 0
2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz = 0
Answer:
0
Step-by-step explanation:
If 2x^2 + 3y^2 + 4z^2 - √6xy - 2√3yz-2√2xz = 0,
then find the value of
(2x^2 + 3y^2 +16z^² +2√6xy - 8√3y2- 8√2xz).