Question

prove that 15-17√2 Is a irrational number

Answer 1

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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)