Question

D= 5 x\(^{10}\) -y \(^{15}\) + 2007 biết (x+1)\(^{2006}\) + (x-1 )\(^{2008}\) =0

Answer 1

\(\left\{{}\begin{matrix}D=5x^{10}-y^{15}+2007\\\left(x+1\right)^{2006}+\left(y-1\right)^{2008}=0\end{matrix}\right.\)

\(\left\{{}\begin{matrix}\left(x+1\right)^{2006}\ge0\forall x\\\left(y-1\right)^{2008}\ge0\forall y\end{matrix}\right.\)

\(\Rightarrow\left(x+1\right)^{2006}+\left(x-1\right)^{2008}\ge0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left(x+1\right)^{2006}=0\\\left(x-1\right)^{2008}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\)

Thay vào biểu thức ta có:

\(D=5.\left(-1\right)^{10}-1^{15}+2007\)

\(D=5-1+2007\)

\(D=2011\)