Ta có:\(\dfrac{x^{2010}+y^{2010}+z^{2010}+t^{2010}}{a^2+b^2+c^2+d^2}=\dfrac{x^{2010}}{a^2}=\dfrac{y^{2010}}{b^2}=\dfrac{z^{2010}}{c^2}=\dfrac{t^{2010}}{d^2}\)
\(\Rightarrow\dfrac{x^{2010}}{a^2}+\dfrac{y^{2010}}{b^2}+\dfrac{z^{2010}}{c^2}+\dfrac{t^{2010}}{d^2}=\dfrac{x^{2010}}{a^2}\)
\(\Rightarrow\dfrac{y^{2010}}{b^2}+\dfrac{z^{2010}}{c^2}+\dfrac{t^{2010}}{d^2}=0\)
\(\Leftrightarrow3\cdot\dfrac{y^{2010}}{b^2}=0\)
\(\Leftrightarrow y^{2010}=0\)
\(\Leftrightarrow y=0\)
CMTT\(\Rightarrow x=z=t=0\)
\(\Rightarrow T=0\)