xyz-x-y-z=5
xyz = 5+ x + y + z
<=> 1 = 1/yz + 1/xz + 1/xy + 5/xyz
giả sử: x ≥ y ≥ z ≥ 1, ta có:
1 = 1/yz + 1/xz + 1/xy + 5/xyz ≤ 1/z^2 + 1/z^2 + 1/z^2 + 5/z^2 = 8/z^2
=> z^2 ≤ 8 => z = 1, 2
*z = 1:
1=1/y + 1/x + 6/xy ≤ 1/y + 1/y + 6/y = 8/y
=> y ≤ 8=> y = 1,2
y =1 => 1=1+7/x suy ra 7/x =0(vô lí)
y = 2 => 1=1/2 +4/x suy ra 4/x=1/2 suy ra x=8
* z = 2
1 = 1/2y + 1/2x + 1/xy + 5/2xy = 1/2y + 1/2x + 7/2xy ≤ 1/2(1/y + 1/y + 7/y) = .9/2y
=> y ≤ 9/2 => y = 1,2
y=1 suy ra 1= 1/2 +8/2x suy ra 8/2x =1/2 suy ra x=1/8 (KTM)
y=2 suy ra 1= 1/4 +9/4y suy ra 9/4y =3/4 suy ra x=1/3 (KTM)
* z =3:
1 = 1/3y + 1/3x + 1/xy + 5/3xy = 1/3y + 1/3x + 8/3xy ≤ 1/3(1/y +1/y + 8/y) = 10/3y
=> y ≤ 10/3 => y = 1,2,3
y = 1 => 1= 1/3 +3x suy ra 3x=2/3 suy ra x=2/9 (KTM)
y=2 suy ra 1=1/6+5/3x suy ra 5/3x=5/6 suy ra x=1/2 (KTM)
Vậy z=1 y=2 x=8
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
