prove
that (5-3√2) is an irrational number, given
that 2 is irrational numben.
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Answer:
Let us assume the contrary.
i.e; 5 + 3√2 is rational
∴ 5 + 3√2 = ab, where ‘a’ and ‘b’ are coprime integers and b ≠ 0
3√2 = ab – 5
3√2 = a−5bb
Or √2 = a−5b3b
Because ‘a’ and ‘b’ are integers a−5b3b 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.
hope it will help you ✌️
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