Question

DAU 100 DE PUNCTE+COROANA!!!!!!!!!!!

Answer 1

Aplici  inegalitatea  mediilor  in toate  exercitiile
Ma≥Mg
1.(x+y)/2≥√xy
(y+z)/2≥√yz
(z+x)/2≥√zx
Le  inmultesti  membru  cu  membru
(x+y)/2*(y+z)/2*(z+x)/8≥√xy*√yz*√zx=√x²y²z²=xyz=>
(x+y)*(y+z)*(x+z)≥8xyz
2.
(x+y)/2≥√xy
(x+z)/2≥√xz
(y+z)/2≥√Yz
______________
(2x+2y+2z)/2≥√xy+√xz+√yz
x+y=z≥√xy+√Xz+√yz
3.Conf  inegalitatii  mediilor  vom  avea
(x+1)/2≥√x
(y+1)/2≥√y
(x+z)/2≥√xz
(y+z)/2≥√yz
________________  inmultesti  inegalitatile  si  obtii
(x+1)*(y+1)*(x+z)*(y+z)≥√x*√y*√xz*√yz
(x+1)*(y+1)*9x+z)*(y+z)/16=√x²y²z²
(x+1)*(y+1)*(x+z)*(y+z)≥16 xyz