Question

Tìm x thuộc Z biết:

86 : [ 2 . ( 2x - 1 )^2 - 7 ] + 4^2 = 2 . 3^2

Answer 1

\(86:\left[2.\left(2x-1\right)^2-7\right]+4^2=2.3^2\)

\(86:\left[2.\left(2x-1\right)^2-7\right]+16=2.9\)

\(86:\left[2.\left(2x-1\right)^2-7\right]=2\)

\(2.\left(2x-1\right)^2-7=43\)

\(2.\left(2x-1\right)^2=50\)

\(\left(2x+1\right)^2=25=5^2=\left(-5\right)^2\)

\(\Rightarrow\orbr{\begin{cases}2x+1=5\\2x+1=-5\end{cases}\Rightarrow\orbr{\begin{cases}2x=4\\2x=-6\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=-3\end{cases}}}\)