Question

[Lê Hạnh Ngân Thanh]

Biết rằng: /a+7/²⁰¹⁷ +/b-3/²⁰¹⁶=0. Tính a-b?

Answer 1

[Lightning Farron]

Ta thấy: \(\left\{{}\begin{matrix}\left|a+7\right|\ge0\forall a\\\left|b-3\right|\ge0\forall b\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\left|a+7\right|^{2017}\ge0\forall a\\\left|b-3\right|^{2016}\ge0\forall b\end{matrix}\right.\)

\(\Rightarrow\left|a+7\right|^{2017}+\left|b-3\right|^{2016}\ge0\forall a,b\)

Nên xảy ra khi \(\left|a+7\right|^{2017}+\left|b-3\right|^{2016}=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|a+7\right|=0\\\left|b-3\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a+7=0\\b-3=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a=-7\\b=3\end{matrix}\right.\)

Suy ra \(a-b=-7-3=-10\)

Answer 2

[Nguyễn Huy Tú]

\(\left|a+7\right|^{2017}+\left|b-3\right|^{2016}=0\)

\(\Rightarrow\left\{{}\begin{matrix}\left|a+7\right|^{2017}=0\\\left|b-3\right|^{2016}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a+7=0\\b-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=-7\\b=3\end{matrix}\right.\)

\(\Rightarrow a-b=-7-3=-10\)

Vậy \(a-b=-10\)