Question

Tính \(2x^5-5y^3+2017\)tại y thỏa mãn \(\left|x-1\right|+\left(y+2\right)^{2016}=0\)

Answer 1

\(\left|x-1\right|+\left(y+2\right)^{2016}=0\)

Ta thấy: \(\hept{\begin{cases}\left|x-1\right|\ge0\\\left(y+2\right)^{2016}\ge0\end{cases}}\)

\(\Rightarrow\left|x-1\right|+\left(y+2\right)^{2016}\ge0\)

\(\Rightarrow\hept{\begin{cases}\left|x-1\right|=0\\\left(y+2\right)^{2016}=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=1\\y=-2\end{cases}}\)

\(\Rightarrow A=2x^5-5y^3+2017=2\cdot1^5-5\cdot\left(-2\right)^3+2017=2059\)