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Solve-x-a-2-2c-2-b-c-x-b-2-2a-2-c-a-x-c-2-2b-2-a-b-0-




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=ya2b2c2y+c2b2b+c+y+a2c2a+c+y+b2a2a+b=0y(1b+c+1a+c+1a+b)=(cb+ac+ba)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+(bc)+x+b2+2a2c+a+(ca)+x+c2+2b2a+b+(ab)=0[(bc)+(ca)+(ab)=0]x+a2+2c2+b2c2b+c+x+b2+2a2+c2a2c+a+x+c2+2b2+a2b2a+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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