Question

prove that 1/3–2√5 is an irrational number.

Answer 1

Answer:

Step-by-step explanation:

We know 2√5 is irrational

let root 1/3 - 2√5 be of the form p/q where p and q are co prime and q is not equal to zero

1/3 - 2√5 = p/q

- 2√5 = p/q - 1/3

2√5 = 1/3 - p/q

2√5 =  q - 3p / 3q

√5 = q - 3p/ 6q

Hence, √5 should be rational from the above eqn.

But we know that √5 is irrational

So, our assumption is incorrect

1/3 - 2√5 is irrational

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Took me a long time to type this

Answer 2

Answer:

We know that 2√5 is an irrational number.

Let 1/3-2√5 is a rational number.

1/3-2√5=p/q. (q#0)

1/-2√5=p/q-1/3

-2√5=q/p-3/1

-√5=q-3p/2p

We know that √5 is an irrational number

our contradiction assumption is false

So,1/3–2√5 is an irrational number.