If w is irrational and v is rational then 3w 5v is

Last updated: 2/12/2024

If w is irrational and v is rational then 3w 5v is irrational Proof Assume 3w 5v is rational then 3w 5v where a b e Z b 0 Then 3w 5v Since is rational then t c de Z and d 0 Then 3t 5 frac ad 5bc bd where ad 5bc bd Z and bd 0 where ad 5bc bd Z and 3bd 0 Hence to Then w is a rational number This is a contradiction The flaw in the previous proof if exists is corrected by assuming that Oate is an irrational number O a 3d w is an irrational number O b god a b 1 Oc a b are positive integers O d w is an irrational number and e is rational