Prove that root 3+5root 7 is an irrational . if root 7 is irrational
Answers
Answered by
2
Answer:
We have to prove that 3+
7
is irrational.
Let us assume the opposite, that 3+
7
is rational.
Hence 3+
7
can be written in the form
b
a
where a and b are co-prime and b
=0
Hence 3+
7
=
b
a
⇒
7
=
b
a
−3
⇒
7
=
b
a−3b
where
7
is irrational and
b
a−3b
is rational.
Since,rational
= irrational.
This is a contradiction.
∴ Our assumption is incorrect.
Hence 3+
7
is irrational.
Hence proved.
Answered by
5
Answer:
let 5-3✓7 be rational
i.e.,5-3✓7=a/b(where a and b are co- prime)
now,5-3✓7=a/b
-3✓7=a/b-7
✓7=(7b-a)/3b
now we know that ✓7 is an irrational number we assume that 5-3✓7 is rational. it is worng thus 5-3✓7 is an irrational number
hence proved
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