Tìm x, y biết (x - 1)^2022 + (căn bậc hai (y - 2))^2023 = 0
Câu hỏi:
Tìm x, y biết (x – 1)2022 + \({\left( {\sqrt {y - 2} } \right)^{2023}} = 0\).
Trả lời:
(x – 1)2022 + \({\left( {\sqrt {y - 2} } \right)^{2023}} = 0\)
Do: \(\left\{ \begin{array}{l}{\left( {x - 1} \right)^{2022}} = {\left[ {{{\left( {x - 1} \right)}^{1011}}} \right]^2} \ge 0\\\sqrt {y - 2} \ge 0 \Leftrightarrow {\left( {\sqrt {y - 2} } \right)^{2023}} = 0\end{array} \right.\)
⇔ (x – 1)2022 + \({\left( {\sqrt {y - 2} } \right)^{2023}} \ge 0\)
Khi (x – 1)2022 + \({\left( {\sqrt {y - 2} } \right)^{2023}} = 0\)
Thì: \(\left\{ \begin{array}{l}x - 1 = 0\\\sqrt {y - 2} = 0\end{array} \right.\)
⇔ \(\left\{ \begin{array}{l}x = 1\\y = 2\end{array} \right.\)
Vậy x = 1; y = 2.
