Question

Given that √5 is irrational, prove that 2√5 − 3is an irrational number

Answer 1

Hello ❤️

Let 2✓5-3 is rational number

so we can find two integers a and b where a and b are two co- prime numbers.

2✓5-3=a/b

-3✓5=a-2b/b

-✓5=a-2b/3

Where -✓5 is an irrational number and a-2b/3 is rational number

Hence ✓5 is an irrational number

This is a contradiction

eg: rational can't equal to irrational

Hence it is an irrational number.

Hope it will help you ☺️

Answer 2

Answer:

Given - √5 is irrational

To prove - (2√5−3) is an irrational number

Property - Rational number is one which can be represented in the form p/q, where q is not equal to 0.

Answer –

As given √5 is irrational.

Now, let us assume that (2√5−3) is a rational number.

We know that rational numbers can be represented in the form of p/q where p & q are integers and q is not equal to 0.

THE REST OF THE WORK IS IN ATTACHMENT:

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