Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Conditional Identities

If a^2 + b^2 + c^2 = 1

Then, fill up the following:

__ < ab+bc+ca < __

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

Re: Conditional Identities

This is attained when

.

By the Cauchy–Schwarz inequality,

This is attained when

.

Hence

.

---

240 books currently added on Goodreads

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Conditional Identities

thanks

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.