Question

prove that 7-2√5 is irrational
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Answer 1

Answer:

ANSWER ➡️

PROVE THAT 7-2 √5 IS IRRATIONAL NUMBER ➡️

Let us assume 7-2√5 is irrational.

Let 7-2√5 =a/b, where a, b are integers and b≠0.

-2√5=(a/b)-7

» )-2√5=(a-7b) /b

»)√5=(a-7b) /(-2b)

=√5=(7b-a)/2-b

Since a, b integers, (7b-a) /2a is rational, and so √5 is rational.

This contradicts the fact that √5 is irrational.

Hence, 7-2√5 is irrational...

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