Find relation between U V W. U=3x+2y-z V=x-2y+z W=x(x+2y-z)

Question

Find relation between U V W.

U=3x+2y-z

V=x-2y+z

W=x(x+2y-z)

Answer 1

From U = 3x + 2y - z => z = 3x + 2y - U.

 

Substitute this value into the other two equations:

V = x - 2y + z = x - 2y + 3x + 2y - U = 4x - U

W = x (x + 2y - z) = x (x + 2y - 3x -2y + U) = x (-2x + U)

 

From V = 4x - U => x = (U + V)/4

Substitute this into the third equation: W = (U + V)/4 *(-U/2 - V/2 + U)

W = (U + V)/4 * (U - V)/2 = (U² - V²)/8

 

This is the relationship between U, V and W