Que. 7 Show that 7-15 is irrational, give that 5 is irrational.

1.	Que. 7 Show that 7-15 is irrational, give that 5 is irrational.
Answer» Let us assume, to the contrary, that 7-√5 is rational That is, we can find Coprime a and b (b≠ 0) such that 7-√5 = a/b Therefore, 7 - a/b = √5 Rearranging this equation √5 = (7b -a)/b since a and b are integers,so (7b -a)/b is an rational. And so √5 is rational But this contradicts the fact that √5 is irrational. This contradiction has arisen because of our incorrect assumption that 7-√5 is rational. Therefore we can conclude that 7-√5 is irrational.

Answer»

Let us assume, to the contrary, that 7-√5 is rational

That is, we can find Coprime a and b (b≠ 0) such that

7-√5 = a/b

Therefore, 7 - a/b = √5

Rearranging this equation √5 = (7b -a)/b

since a and b are integers,so (7b -a)/b is an rational.

And so √5 is rational

But this contradicts the fact that √5 is irrational.

This contradiction has arisen because of our incorrect assumption that 7-√5 is rational.

Therefore we can conclude that

7-√5 is irrational.

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