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Đặt `x/a=y/b=z/c=k (k \ne 0)`
`->x=ak, y=bk, z=ck`
Có : `(x^2 + y^2+z^2) (a^2x + b^2y + c^2z)`
`= (a^2k^2 + b^2k^2 +c^2k^2) (a^3k + b^3k + c^3k)`
`= k^2 (a^2 + b^2 +c^2) k (a^3 + b^3 +c^3)`
`= k^3 (a^2 + b^2 +c^2) (a^3 + b^3+c^3)`
Có : `(a^2 + b^2 +c^2) (x^3 + y^3 + z^3)`
`= (a^2 + b^2 +c^2) (a^3k^3 + b^3k^3 + c^3k^3)`
`= (a^2 +b^2+c^2) k^3 (a^3 + b^3 +c^3)`
`= k^3 (a^2 + b^2+c^2)(a^3 + b^3+c^3)`
`P = ( (x^2 + y^2+z^2) (a^2x + b^2y + c^2z) )/( (a^2 + b^2 +c^2) (x^3 + y^3 + z^3) )`
`-> P= ( k^3 (a^2 + b^2 +c^2) (a^3 + b^3+c^3) )/( k^3 (a^2 + b^2 +c^2) (a^3 + b^3+c^3) )`
`-> P= 1`
Vậy `P=1` khi `x/a=y/b=z/c`
