Question

again , pissed off , not getting what is the problem trying to say

Answer 1

what is alpha and beta ? rational or irrational wtf

Answer 2

@ikram002p

Answer 3

there is a typo in the question, it should say \(\large \beta \ne 0\)

Answer 4

alpha is rational and beta is irrational

Answer 5

actually^^

Answer 6

how ikram

Answer 7

a rational number is a number that can be expressed as the ratio of integers.
an irrational number is a number that cannot be expressed as the ratio of integers.

Answer 8

ganesh both should not equal zero since if alpha =0
then
alpha. beta =0 rational
0/beta =0 rational

Answer 9

actually alpha also should not be =0

Answer 10

agree

Answer 11

no, \(\alpha \ne 0\) is correct. 0 is rational, not irrational

Answer 12

how ever prove by contradiction
assume
a/b = h/d ( rational )

ad=hb
b=ad/h (contradiction )

same ith product

Answer 13

Actually i didn't get what the problem says

Answer 14

lol no mood for typing xD

Answer 15

given :

"a" is a non zero rational number, and b is an irrational number.

to prove :

ab and a/b are irrational

Answer 16

notice that b also cannot be 0

Answer 17

makes sense

Answer 18

yes otherwise the fraction ..............

Answer 19

b already cant be 0 , cuz of the given it irrational hehe
i dint note that

Answer 20

so u know how to prove nw ha ?

Answer 21

i need a new brain :o

Answer 22

lol no ikram

Answer 23

ermm wanna switch xD

Answer 24

i 'm solving a new book online free o cost incase anyone wants to try
http://iitjeelibrary.blogspot.in/

Answer 25

okay back to the problem

Answer 26

why a is rational ?

Answer 27

it is given

Answer 28

sry yes

Answer 29

ok in short
u are given that a is non zero rational
and b is irrational

first wanna prove
a.b is also irrational

prove by contradiction
let a.b rational
then a.b=c/d
b=c/da which is a contradiction since b is given to be irrational

Answer 30

got it now ?

Answer 31

coooool!

Answer 32

ok , same idea with a/b

Answer 33

how

Answer 34

prove by contradiction
let a/b be rational
then
a/b=c/d
then b=ad/c contradiction

Answer 35

sorry yes