**Problem ** Let x, y, z be real numbers such that . Prove that

**Discussion**

Note that .

According to the given condition .

Therefore .

Adding 2(x+y+z) + 1 to both sides,

We wish to show

or

Replacing 2xyz by we have

(this is what we need to show).

Therefore we need to show

This is true by Cauchy Schwarz Inequality.

PROOF 2 (suggested by Arkabrata Das)

CHECK FILE: new doc 1720151229235503023

## Chatuspathi:

**Paper:**RMO 2015 (Mumbai Region)**What is this topic:**Inequality**What are some of the associated concepts:**Cauchy Schwarz Inequality**Where can learn these topics:**Cheenta**Book Suggestions:**Secrets in Inequalities

please give the solution of a sum from walker and miller

PQRS is a square. T is any point on PR. Perpendiculars TA and TB are drawn on PS and PQ respectively.

TW is drawn perpendicular to AQ and RZ is drawn perpendicular to AQ. Prove that AW=ZQ.

please give the solution of this sum adopted from walker and miller

please solve that second and third question of prmo 2015