Question

Prove that 15 + 17√15
is an
irrational number​

Answer 1

Step-by-step explanation:

let us assume that 15 +17√5 is a rational no. where 15 +17√5 =a/b,where a and v are Coprime, b is not equal =0

> 15+17√5=a/b

>17√5=a/b -15

>√5=a-15b/17b

therefore a and b are integers.

so, a-15b/17b is a rational no. and so, √5 is rational.

but this contradicts the fact that √5 is irrational. This contradiction has arisen because of our incorrect assumption that 15 +17√5 is rational.

hence, 15+17√5 is irrational.

Let's assume 15+17√5is a rational number so-

15+17√5=p/q

√5= p/q-15÷17

because √3 is an irrational number and p/q-15÷17 will be a rational number but irrational number can't be equal to rational number thus we have assumed wrong.

hence 15+17√5 is an irrational number.

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