prove it (imp 4 jee)

u can add 3 on both sides ..
then this becomes d A.M > H.M inequality dats d simplest proof !

EDIT : well, even i know juz 2

lets move on Proof No 2

we have

x²/xz+xy +y²/xy+yz + z²/xz+yz ≥3/2

Applying Cauchy we get

(x+y+z)²/2(x+y+z)≥3/2

x²+y²+z²â‰¥xy+yz+xz
1/2[(x-y)²+(y-z)²+(x-z)²]≥0

hence proved

by symmetry minima if exists is at x=y=z

so put x=y=z u get ans≥3/2

awesome post mirka
thanx 4 the link
now its party (inequality )time