prove that 5+3√2 is an irrational number
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Answered by
2
Answer:
Let us assume the contrary.
i.e; 5 + 3√2 is rational
∴ 5 + 3√2 =
a
b
, where ‘a’ and ‘b’ are coprime integers and b ≠ 0
3√2 =
a
b
– 5
3√2 =
a−5b
b
Or √2 =
a−5b
3b
Because ‘a’ and ‘b’ are integers
a−5b
3b
is rational
That contradicts the fact that √2 is irrational.
The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.
So, 5 + 3√2 is irrational.
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Answered by
1
Answer:
Let us consider that 5+3√2is rational
⇒5+3√2=p/q
where
p and q are co prime
q≠0
p and q are integers
5+3√2=p/q
⇒3√2=p/q-5
⇒3√2=p-5q/q
⇒√2=p-5q/3q
√2 is irrational but p-5q/3q is rational
This contradicts that our supposition is wrong
∴ 5+3√2 is irrational
Step-by-step explanation:
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