1 ( + AC BD + )2 = ( AD − BC )2+ ( AC BD + )2 = ( A2+ B2)( C2+ D2)ÁP...

Bài 7:Lời Giải: Ta có:

^{1 ( + ac bd + )}

²

^{= ( ad − bc )}

²

⁺ ( ^{ac bd +} )

²

⁼ ( ^a

²

^{+ b}

²

)( ^c

²

^{+ d}

²

)

Áp Dụng BĐT AM-GM ta có:

( ^a

²

^{+ b}

²

) ( ^{+ c}

²

^{+ d}

²

) ^{≥ 2} ( ^a

²

^{+ b}

²

)( ^c

²

^{+ d}

²

) ^{= 2 1 ( + ac bd + )}

²

Khi ñó Chuyển ac bd+ =x thì

P ≥ 2 1 + x

²

+ x

→ = + + + + = + + + + +

2

2

2

2

2

2

2

4(1 ) 4 1 3 [(2 ) 4 1 (1 )]P x x x x x x x x

( )

²

→ = + + + ≥ → ≥ → ≥P 3 (Q.E.D)

2

2

3 2 1 3 3P x x P