Question

prove that 2-3√5 is an irrational number​

Answer 1

Step-by-step explanation:

Let 2-3√5 is a rational number

So, it can be written in p/q form where p and q are co- prime integers and q is not equal to 0.

2-3√5 =p/q

3√5=p/q-2

3√5 =2p-q/q

√5=2p-q/3q

So p&q are integers

So, 2p-q/3q is a rational number,

Also, √5 is also a rational number

So it leads to contradiction

But we know that √5 is a irrational number

So, 2-3√5 is an irrational number

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