CÂU 5 NỘI DUNG ĐIỂM
1,0 đ
Áp d ụ ng b ất đẳ ng th ứ c Cauchy ta có:
2
2
2
2 2 2
x yz y zx z xy
≥ + +
H
+ + +
y y z z z z x x x x y y
x x xyz y y xyz z z xyz
= + +
0,25 đ
x x y y z z
= − + +1 2 4( )
x x a b c = + 2 9a y y z z = + ⇒ = − +2 1 2 4Đặ t:
b z z x x y y a b c9 = + c x x y y2 1 = + −z z a b c4 2Khi đó
− + + − + + − a b c a b c a b c2 2 4 2 4 4 2≥ + + H a b c b a c c a b2 6 4= − + + + + + + a c a a b c b a c c a b2 6 4.3. 3.≥ − + ⋅ ⋅ + ⋅ ⋅ 3
3
a c a a b c =2