Math, asked by shboy, 11 months ago

if 2 X square + 3 y square + 4 x square minus root 6 x y minus 2 root 3 y z minus 2 root 2 X is equals to zero then find the value of 2 X square + 3 y square + 16 Z square + 2 root 6 x y - 3 Y Z - 8 root 2 x z ​

Answers

Answered by amitnrw
12

Given :  2x² + 3y²  + 4z² - √6xy - 2√3yz  - 2√2xz  = 0

To find : 2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz

Solution:

2x² + 3y²  + 4z² - √6xy - 2√3yz  - 2√2xz  = 0

=> 2(2x² + 3y²  + 4z² - √6xy - 2√3yz  - 2√2xz ) = 0

=> 2x²  + 3y² - 2√6xy  +  3y²  + 4z²  - 4√3yz + 2x² + 4z² - 4√2xz = 0

=> (√2x - √3y)²  + (√3y - 2z)² + (√2x  - 2z)² = 0

as each term is square and sum of all terms = 0

hence each term =  0

=> √2x - √3y = 0 ,  √3y - 2z = 0  , √2x  - 2z = 0

=> √2x = √3y  ,  √3y = 2z   , √2x =  2z  

=> √2x = √3y = 2z

=> 2x² = 3y² = 4z²

2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz

= 2x² +  2x² + 4(2x²) + 2√2x√3y  - 8(√2x )(√2x/2)   - 8√2x (√2x /2)

= 4x²  + 8x²  + 2√2x√2x  - 8x²   - 8x²

= -4x²  + 4x²

= 0

2x² + 3y² + 16z² + 2√6xy - 8√3yz - 8√2xz = 0

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Answered by manthan0
4

if the answer is write mark as brainliest

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