Question

Prove that (2-3√5) is irrationl

Answer 1

Answer:

let 2-3√5 be a rational number.

→2-3√5=p/q(where p and q are co. primes and qis not equal to zero)

→-3√5=p/q-2

→3√5=p-2q/q

→√5=p-2q/3q

→irrational number=rational number

but this is not possible and it contradicts our assumption that 2-3√5 is rational number.

hence 2-3√5 is an irrational number

Answer 2

Answer:

Assume 2-3√5 be a rational no

therefore 2-3√5=a/b

hence √5=a-2b/3b

therefore a-2b/3b is a rational no

therefore √5 is a rational no

but we know that √5 is a irrational no

therefore our assumption was wrong that 2-3√5 is a rational no

therefore 2-3√5 is a irrational no...

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