Question

Prove that 15+17√2 be an irrational number

Answer 1

Let 15+17√2 is a rational number
we know that any rational no. it is in the form of p/q ,where pand q are co-prime no.
15+17√2=p/q
17√2=p/q -15
√2=p-15q/17q ...........(I)
here, p and q are some integers
therefore, p-15q/17q is a rational no.
but, √2 is irrational no.
it contradicts our supposition
=> 6+√2 is irrational .............(hence proved)

Answer 2

Answer:

Step-by-step explanation:   hello

Let 15+17√2 is a rational number

we know that any rational no. it is in the form of p/q ,where pand q are co-prime no.

15+17√2=p/q

17√2=p/q -15

√2=p-15q/17q ...........(I)

here, p and q are some integers

therefore, p-15q/17q is a rational no.

but, √2 is irrational no.

it contradicts our supposition

=> 6+√2 is irrational .............(hence proved)