Let p ∈ Q be a rational number such that p > 1 and letq := pp − 1 .Prove that for all a, b ≥ 0,ab ≤ app + bqq

Question

Let p ∈ Q be a rational number such that p > 1 and letq := pp − 1 .Prove that for all a, b ≥ 0,ab ≤ app + bqq
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Solution 1

To prove that for all a, b ≥ 0, ab ≤ app + bqq, we can start by rearranging the inequality.

First, let's substitute q with pp - 1:

ab ≤ app + b(pp - 1)(pp - 1)

Next, we can expand the right side of the inequality:

ab ≤ app + b(p^2p^2 - 2pp + 1)

Simplifying further:

ab ≤ app + bp^4 - 2bp^3 + b Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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