Question

prove that 4-2√5 is an irrational number.​

Answer 1

Let us assume that

(4−

5

2

)

is rational .

Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.

4−

(4−

5

2

)

is rational

⇒5

2

is rational

which is only possible if

5

is rational and

2

is rational.

As we know prouduct of two rational number s rational

But the fact is

2

is an irrational.

Which is contradictory to our assumption.

Hence,

4−5

2

is irrational . hence proved.

Answered By

toppr

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