Đáp án:
`a)`
` => 2x^2 + 2y^2 + 2z^2 \ge 2xy + 2yz + 2xz`
` => 2x^2 + 2y^2 +2z^2 - 2xy - 2yz -2xz \ge 0`
` => (x^2 -2xy + y^2) + (y^2 - 2yz + z^2) + (z^2 -2zx + x^2) \ge 0`
` => (x-y)^2 + (y-z)^2 + (z-x)^2 \ge 0` ( đpcm )
Dấu `=` xảy ra khi ` x = y=z`
`b)`
Ta có ` x^4 = (x^2)^2 ; y^4 = (y^2)^2 ; z^4 = (z^2)^2`
` => x^4+ y^4 +z^4 \ge x^2*y^2 + y^2* z^2 + z^2*x^2 = (xy)^2 + (yz)^2 +(zx)^2`
` \ge xy*yz + yz * zx + xy * zx = xy^2z + xyz^2 + x^2yz = xyz (x+y+z)`
Dấu `=` xảy ra khi ` x = y= z `
