Question

tìm x biết \(\text{(x^2-3)^2 = 16}\)

Answer 1

Theo đề ta có:

\(\left(x^2-3\right)^2=16\)

=> \(\left[{}\begin{matrix}\left(x^2-3\right)^2=4^2\\\Rightarrow x^2-3=\left(-4\right)\\\Rightarrow x^2-3=4\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x^2-3=-4\\\Rightarrow x^2=\left(-4\right)+3\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x^2-3=4\\\Rightarrow x^2=4+3\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x^2=\left(-4\right)+3\\\Rightarrow x^2=4+3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x^2=\left(-1\right)\\x^2=7\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=\sqrt{-1}\\x=\sqrt{7}\end{matrix}\right.\)