Question

[Hot Girl]

Tìm x,y,z biết:

|2x^2-27|^2019+(5y+12)^2018=0

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Answer 1

[Tẫn]

\(\left|2x^2-27\right|^{2019}+\left(5y+12\right)^{2018}=0.\)

\(\text{Ta có}\hept{\begin{cases}\left|2x^2-27\right|^{2019}\ge0\\\left(5y+12\right)^{2018}\ge0\end{cases}}\text{Mà}\left|2x^2-27\right|^{2019}+\left(5y+12\right)^{2018}=0\)

\(\Rightarrow\hept{\begin{cases}\left|2x^2-27\right|^{2019}=0\\\left(5y+12\right)^{2018}=0\end{cases}\Rightarrow\orbr{\begin{cases}\left(2x-27\right)^{2019}=0\\\left(5y+12\right)^{2018}=0\end{cases}\Rightarrow\orbr{\begin{cases}2x-27=0\\5y+12=0\end{cases}\Rightarrow\orbr{\begin{cases}2x=27\\5y=-12\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{27}{2}\\y=\frac{-12}{5}\end{cases}}}}}}\) 

\(\text{Vậy}\hept{\begin{cases}x=\frac{27}{2}\\y=\frac{-12}{5}\end{cases}}\)