Determine the largest interval \(\displaystyle{]}\alpha,+\infty{[}\) such that

Sanai Huerta

Sanai Huerta

Answered question

2022-03-27

Determine the largest interval ]α,+[ such that 1a+1b+1a2+b2<1 for every, a,b]α,+[?

Answer & Explanation

tabido8uvt

tabido8uvt

Beginner2022-03-28Added 16 answers

Assume a=b=x such that
1a+1b+1a2+b2=2x+12x2=12+12=x
Now observe that
f(a,b)=1a+1b+1a2+b2
is decresing with a and b therefore α=2+12.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?