0 Ê (X - Y)2+ (Y - Z)2+ (Z - X)2== 2(X2+ Y2+ Z2) - 2(XY + YZ + ZX) == 2 - 2(XY + YZ + ZX) Ị XY + YZ + ZX Ê 1

2 . - DAP AN DE LUYEN THI TNDH30 2 . - DAP AN DE LUYEN THI TNDH30
DAP AN DE LUYEN THI TNDH30

2 .

Mặt khác lại có:

0 Ê (x - y)

2

+ (y - z)

2

+ (z - x)

2

== 2(x

2

+ y

2

+ z

2

) - 2(xy + yz + zx) == 2 - 2(xy + yz + zx) ị xy + yz + zx Ê 1.

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Câu IVa.

1 1 2

 

dx dx 1 1

dx 1 1

= ∫ + + ∫ + − ∫   + − +  

= ∫ + + = ∫   + − +  

1 2 1 2 1

I dx

2 dx

2

x 1 x 2

(x 1) (x 2)

[(x 1)(x 2)]

0 00 0 0

2

= 3 + 2ln3 − 4ln2

Câu Va.