Ta có:\(\left(ay-bx\right)^2\ge0\Leftrightarrow a^2y^2-2axby+b^2x^2\ge0\)
\(\Leftrightarrow a^2y^2+b^2x^2\ge2abxy\)
\(\Leftrightarrow a^2x^2+a^2y^2+b^2y^2+b^2x^2\ge a^2x^2+2abxy+b^2y^2\)
\(\Leftrightarrow\left(a^2+b^2\right).\left(x^2+y^2\right)\ge\left(ax+by\right)^2\)
Vậy...