So, there exist co-prime integers a and b where b ≠ 0
a
b
=
Cubing on both sides, we get
5
=
a3
b3
⇒
5
=
a3
b3
∴
5 divides a3 ⇒ 5 divides a
∴
5 is a factor of a
…from (1)
Let
a
=
5c
∴
b3
=
5c
5
∴
b3
=
5
5
×
5
×
5c3
∴
b3
5
=
5c3
∴
5 divides b3 ⇒ 5 divides 5.
∴
5 is a factor of b
… (3)
From (2) and (3)
5 is a common factor of a and b
∴
a and b are not co-prime
∴
our assumption is wrong
∴
Sol.
Q.
such that
[
a
b
=
[ ]
3
∴
]3
a
b
3
b3
5
( )3
… (1)
… (2)