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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Cho a/b+c +b/a+c + c/a+b =1 CMR: a^2/b+c + b^2/a+c + c^2/a+b =0

Toán Lớp 8: Cho a/b+c +b/a+c + c/a+b =1
CMR: a^2/b+c + b^2/a+c + c^2/a+b =0

Comments ( 2 )

  1. $\\$
    a^2/(b+c)+b^2/(a+c)+c^2/(a+b)
    =a . a/(b+c)+ b . b/(a+c)+ c . c/(a+b)
    = a . (a/(b+c)+1-1) + b.  (b/(a+c)+1-1) + c . (c/(a+b) + 1-1)
    = a . (a/(b+c) + (b+c)/(b+c) – 1) + b  . (b/(a+c)+(a+c)/(a+c)-1) + c . (c/(a+b)+(a+b)/(a+b)-1)
    =a . ((a+b+c)/(b+c) – 1) + b . ((a+b+c)/(a+c)-1) + c . ((a+b+c)/(a+b)-1)
    = a . (a+b+c)/(b+c) – a + b . (a+b+c)/(a+c) – b + c . (a+b+c)/(a+b) – c
    = (a+b+c) (a/(b+c) + b/(a+c) + c/(a+b)) – (a+b+c)
    = a+b+c – (a+b+c)
    = 0 (đpcm)

  2. Giải đáp:
     
    Lời giải và giải thích chi tiết:
     Ta có :
    a/(b+c)+b/(a+c)+c/(a+b)=1
    =(a+b+c)(a/(b+c)+b/(a+c)+c/(a+b))=a+b+c
    =a^2/(b+c)+b^2/(a+c)+c^2/(a+b)+(ab+bc)/(c+a)+(ac+bc)/(a+b)+(ab+ac)/(b+c)=a+b+c
    =a^2/(b+c)+b^2/(a+c)+c^2/(a+b)+b+c+a=a+b+c
    =a^2/(b+c)+b^2/(a+c)+c^2/(a+b)=0(đpcm)
    #Ken

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222-9+11+12:2*14+14 = ? ( )

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