Question

[nguyễn hà]

cho các số a,b,c,d\(\ne\)0 . tính:

T= \(x^{2011}+y^{2011}+z^{2011}+t^{2011}\)

biết x,y,z,t thỏa mãn:

\(\dfrac{x^{2010}+y^{2010}+z^{2010}+t^{2010}}{a^2+b^2+c^2+d^2}=\dfrac{x^{2010}}{a^2}+\dfrac{y^{2010}}{b^2}+\dfrac{z^{2o1o}}{c^2}+\dfrac{t^{2010}}{d^2}\)

Answer 1

[Phạm Nguyễn Tất Đạt]

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\(\Rightarrow x=z=t=0\)

\(\Rightarrow T=0\)