- #1
drago
- 6
- 0
Hi,
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
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