Nhận xét: 3. (x2 + y2 + z2) = 2,25
(x+y+z)2 = 2,25
=> 3. (x2 + y2 + z2) = (x+y+z)2
=>3x2 + 3y2 + 3z2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
=> 2x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx = 0
=> (x2 - 2xy + y2 ) + (y2 - 2yz + z2) + (z2 - 2xz + x2) = 0
=> (x-y) 2 + (y - z)2 + (z-x)2 = 0
=> x - y = y - z = z - x = 0
=> x = y = z => x = y = z = 1,5/3 = 0,5
ta có:
(x+y+z)2=x2+y2+z2+2xy+2xz+2yz
=>1,52=0,75+2.(xy+xz+yz)
=>xy+xz+yz=0,75
=>xy+xz+yz=x2+y2+z2
=>2xy+2xz+2yz=2x2+2y2+2z2
<=>2x2+2y2+2z2-2xy-2xz-2yz=0
<=>x2-2xy+y2+x2-2xz+z2+y2-2yz+z2=0
<=>(x-y)2+(x-z)2+(y-z)2=0
<=>x-y=0 và x-z=0 và y-z=0
<=>x=y=z
=> x+y+z=1,5 hay x+x+x=1,5
<=>3x=1,5
<=>x=0,5
Vậy x=y=z=0,5
Bài làm
(x+y+z)2 = 2,25
=> 3. (x2 + y2 + z2) = (x+y+z)2
=>3x2 + 3y2 + 3z2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
=> 2x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx = 0
=> (x2 - 2xy + y2 ) + (y2 - 2yz + z2) + (z2 - 2xz + x2) = 0
=> (x-y) 2 + (y - z)2 + (z-x)2 = 0
=> x - y
= y - z
= z - x = 0
=> x = y = z
=> x = y = z = 1,5/3 = 0,5
hok tốt
