Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I would appreciate some ideas on the following problem:

We are given the inequality:

(1)

|a| + |b| >= 2(|c| + |d|)

Can we conclude that:

(2)

(c + a)^2 + (d + b)^2 >= c^2 + d^2 ?

a, b, c, d are real.

I can prove (2) if (1) is in the form: |a| + |b| >= 4max(|c|,|d|), but the above is stronger.

Thank you.

drago

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inequality problem

**Physics Forums | Science Articles, Homework Help, Discussion**