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Question Number 70598 by Shamim last updated on 06/Oct/19

If a,b,c ∈ ℜ and (a^2 /(b+c))+(b^2 /(c+a))+(c^2 /(a+b))=((12)/(a+b+c))  , (a/(b+c))+(b/(a+c))+(c/(a+b))=(4/3) then find a+b+c=?

Ifa,b,canda2b+c+b2c+a+c2a+b=12a+b+c,ab+c+ba+c+ca+b=43thenfinda+b+c=?

Answered by som(math1967) last updated on 06/Oct/19

(a^2 /(b+c)) +a+(b^2 /(c+a)) +b +(c^2 /(c+a)) +c−(a+b+c)                                                              =((12)/(a+b+c))  ((a(a+b+c))/(b+c)) +((b(a+b+c))/(c+a))+((c(a+b+c))/(a+b))                                     −(a+b+c)=((12)/(a+b+c))  (a+b+c)((a/(b+c)) +(b/(c+a)) +(c/(a+b)) −1)=((12)/(a+b+c))  (a+b+c)((4/3) −1)=((12)/(a+b+c))   ★  (((a+b+c)^2 )/3)=12  (a+b+c)^2 =36 ⇒(a+b+c)=±6  ★(a/(b+c)) +(b/(c+a)) +(c/(a+b)) =(4/3)

a2b+c+a+b2c+a+b+c2c+a+c(a+b+c)=12a+b+ca(a+b+c)b+c+b(a+b+c)c+a+c(a+b+c)a+b(a+b+c)=12a+b+c(a+b+c)(ab+c+bc+a+ca+b1)=12a+b+c(a+b+c)(431)=12a+b+c(a+b+c)23=12(a+b+c)2=36(a+b+c)=±6ab+c+bc+a+ca+b=43

Commented by Shamim last updated on 06/Oct/19

tnks

tnks

Commented by Rasheed.Sindhi last updated on 06/Oct/19

∨  ⊓∣⊏∈!

⊏∈!

Commented by som(math1967) last updated on 06/Oct/19

Nice use of mathematical symbols

Niceuseofmathematicalsymbols

Commented by peter frank last updated on 06/Oct/19

good

good

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