[tex]a + b + c = 2006[/tex]
[tex]ax+by+cz = 0[/tex]
\Rightarrow [tex] (ax+by+cz)^2 = 0[/tex]
\Leftrightarrow [tex] a^2x^2 + b^2y^2 + c^2z^2 = -2axby - 2bycz - 2axcz (*) [/tex]
[tex]C =\frac{ax^2 + by^2 + cz^2 }{ab(x-y)^2+bc(y-z)^2+ca(z-x)^2}[/tex]
\Leftrightarrow[tex]C = \frac{ax^2 + by^2 + cz^2 }{abx^2-2abxy+aby^2+bcy^2-2bcyz+bcz^2+caz^2-2cazx+cax^2}[/tex]
[tex] Thay (*) vao C [/tex]
\Leftrightarrow[tex]C = \frac{ax^2 + by^2 + cz^2 }{abx^2+aby^2+bcy^2+bcz^2+caz^2+cax^2+a^2x^2 + b^2y^2 + c^2z^2}[/tex]
\Leftrightarrow[tex]C = \frac{ax^2 + by^2 + cz^2 }{(abx^2 + cax^2 + a^2x^2)+(aby^2+bcy^2+b^2y^2)+(bcz^2 + caz^2 + c^2z^2)}[/tex]
\Leftrightarrow[tex]C = \frac{ax^2 + by^2 + cz^2 }{ax^2(b + c + a) + by^2(a + c + b) + cz^2( b + a + c )}[/tex]
\Leftrightarrow[tex]C=\frac{ax^2 + by^2 + cz^2 }{( a + b + c)(ax^2 + by^2 + cz^2 )}[/tex]
\Leftrightarrow [tex]C= \frac{1}{( a + b + c)}[/tex]
\Leftrightarrow [tex]C= \frac{1}{2006}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
