wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

Question 14
Prove that p+q is irrational, where p and q are primes.


Open in App
Solution

Let us suppose that p+q is rational.
Again, let p+q=a, where a is rational.
Therefore, q=ap
On squaring both sides, we get
q= a2+p2ap [ (ab)2=a2+b22ab]
Therefore, p=a2+pq2a.

This contradicts our assumption, as the right-hand side is a rational number whereas p is irrational.
Hence, p+q is irrational.


flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon