Cho a+b+c = 0; x+y+z=0; a/x +b/y +c/z = 0 CMR ax ² + by ² + cz ² = 0

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1. `bossthai02`

   Từ `x+y+z=0` 

   `⇒x^2=(y+z)^2,  y^2=(x+z)^2,  z^2=(x+y)^2`

   Mặt khác :

   `ax^2+by^2+cz^2`

   `=a(y+z)^2+b(x+z)^2+c(x+y)^2`

   `=a(y^2+2yz+z^2)+b(x^2+2xz+z^2)+c(x^2+2yx+x^2)`

   `=x^2(b+c)+y^2(a+c)+z^2(a+b)+2(ayz+bxz+cxy)`

   `=-(ax^2+by^2+cz^2)+2(ayz+bxz+cxy)`

     mà ` ayz+bxz+cxy=0( vìa/x +b/y +c/z = 0)`

   `⇒ ax^2+by^2+cz^2=-ax^2-by^2-cz^2` 

   `⇒ 2(ax^2+by^2+cz^2)=0`

   `⇒(ax^2+by^2+cz^2)=0`

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