Ta có :
`x/a + y/b + z/c = 0 (a;b;c \ne 0)`
`=> (xbc)/(abc) + (yac)/(abc) + (zab)/(abc) = 0`
`=> (xbc + yac + zab)/(abc) = 0 `
Mà `abc \ne 0` (do `a ; b ; c \ne 0`)
`=> xbc + yac + zab = 0`
Ta lại có :
`a/x + b/y + c/z = 2 (x ; y ; z \ne 0)`
`=> (a/x + b/y + c/z)^2 = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 2 ( (ab)/(xy) + (ac)/(xz) + (bc)/(yz) ) = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 2 ( (abz)/(xyz) + (acy)/(xyz) + (bcx)/(xyz) ) = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 2 (abz + acy + bcx)/(xyz) = 4`
Mà `xbc + yac + zab = 0` (cmt)
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 2 . 0/(xyz) = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 2 . 0 = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) + 0 = 4`
`=> (a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) = 4`
Vậy `(a^2)/(x^2) + (b^2)/(y^2) + (c^2)/(z^2) = 4`
