Question

If ` x prop yz ` and ` y prop zx, ` then prove that z is a non- zero variation constant.

Answer 1

`x prop yz rArr x = k_1 .yz (k_1 ne 0 =` variation constant )
`rArr y= x/(k_1z)…… (I) `
again `y prop zx rArr y = k_2 .zx (k_2 ne 0 = ` variation constant ) `rArr x/(k_1z)=k_2.zx [ " from (1)"] `
`rArr z^2 = k_1k_2rArr z = sqrt(k_1k_2) ........(2)`
since `k_1.k_2 ` are non-zero variation constants.
`therefore sqrt (k_1k_2)` is an non- zero variation constant.
`rArr z ` is a non-zero variation constant.
Hence z is a non-zero variation constant