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Question Number 182131 by Agnibhoo98 last updated on 04/Dec/22

Solve ((x + a^2 + 2c^2 )/(b + c)) + ((x + b^2 + 2a^2 )/(c + a)) + ((x + c^2 + 2b^2 )/(a + b)) = 0

Solvex+a2+2c2b+c+x+b2+2a2c+a+x+c2+2b2a+b=0

Answered by manxsol last updated on 04/Dec/22

x=y−a^2 −b^2 −c^2 ((y+c^2 −b^2 )/(b+c))+((y+a^2 −c^2 )/(a+c))+((y+b^2 −a^2 )/(a+b))=0 y((1/(b+c))+(1/(a+c))+(1/(a+b)))=−(c−b+a−c+b−a) y=0 x=−(a^2 +b^2 +c^2 )

x=y−a2−b2−c2y+c2−b2b+c+y+a2−c2a+c+y+b2−a2a+b=0y(1b+c+1a+c+1a+b)=−(c−b+a−c+b−a)y=0x=−(a2+b2+c2)

Answered by Rasheed.Sindhi last updated on 05/Dec/22

((x+a^2 +2c^2 )/(b+c))+((x+b^2 +2a^2 )/(c+a))+((x+c^2 +2b^2 )/(a+b))=0 ((x+a^2 +2c^2 )/(b+c))+(b−c) +((x+b^2 +2a^2 )/(c+a))+(c−a) +((x+c^2 +2b^2 )/(a+b))+(a−b)=0 [∵(b−c)+(c−a)+(a−b)=0] ((x+a^2 +2c^2 +b^2 −c^2 )/(b+c)) +((x+b^2 +2a^2 +c^2 −a^2 )/(c+a)) +((x+c^2 +2b^2 +a^2 −b^2 )/(a+b))=0 ((x+a^2 +b^2 +c^2 )/(b+c))+((x+a^2 +b^2 +c^2 )/(c+a))+((x+a^2 +b^2 +c^2 )/(a+b))=0 (x+a^2 +b^2 +c^2 )((1/(b+c))+(1/(c+a))+(1/(a+b)))=0 x+a^2 +b^2 +c^2 =0 x=−(a^2 +b^2 +c^2 )

x+a2+2c2b+c+x+b2+2a2c+a+x+c2+2b2a+b=0x+a2+2c2b+c+(b−c)+x+b2+2a2c+a+(c−a)+x+c2+2b2a+b+(a−b)=0[∵(b−c)+(c−a)+(a−b)=0]x+a2+2c2+b2−c2b+c+x+b2+2a2+c2−a2c+a+x+c2+2b2+a2−b2a+b=0x+a2+b2+c2b+c+x+a2+b2+c2c+a+x+a2+b2+c2a+b=0(x+a2+b2+c2)(1b+c+1c+a+1a+b)=0x+a2+b2+c2=0x=−(a2+b2+c2)

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