4 4 4 1 ( 2 2 2)2A + B + C = 2 A + B + C BÀI 10

Bài 100: Cho a+b+c=0, CMR:

¹ (

)

a + b + c = 2 a + b + c Bài 10: CMR: Nếu ^{1 1 1} 3

a + + = b c và

a+b+c=abc . Thì ta có: ¹

¹

¹

7

a + b + c =

HD :

Ta có : ( ^{a b c + +} )

^{=  0 a}

^{+ b}

^{+ + c}

² ( ^{ab bc ca + +} ) ^{=  0 a}

^{+ b}

^{+ c}

^{= − 2} ( ^{ab bc ca + +} )

( ^a

^{+ b}

^{+ c}

)

^{= 4 ( ab bc ca + + )}

( ) ( ( ) )

 + + + + + = + + + + +

2 4 2

a b c a b b c c a a b b c c a abc a b c

 ^a

^{+ b}

^{+ c}

^{= 2} ( ^{a b}

^{+ b c}

^{+ c a}

) ^{ 2} ( ^a

^{+ b}

^{+ c}

) ^{= a}

^{+ b}

^{+ + c}

^{2 a b}

^{+ 2 b c}

^{+ 2 c a}

(

) (

)

 + + = + + => ĐPCM

2 a b c a b c