find relation between x,y and z x² + 4y² + 9z² - 2xy - 3xz - 6yz = 0

Asked by sundramsingh1707 | 11th Jun, 2022, 05:20: PM

Expert Answer:

x3 + (2y)3 + (3z)3 - x (2y) (3z)  = ( x+ 2y + 3z) ( x2 + 4y2 + 9z2 - 2xy - 6yz -3xz )
 
since ( x2 + 4y2 + 9z2 - 2xy - 6yz -3xz ) = 0 , LHS of above expression is zero
 
Hence we get , x3 + (2y)3 + (3z)3  =  x (2y) (3z)  = 6xyz

Answered by Thiyagarajan K | 12th Jun, 2022, 11:11: AM