Question

(x - \(\dfrac{3}{2}\))² + \(\dfrac{1}{2}\) = \(\dfrac{9}{2}\)

Answer 1

`(x-3/2)^2 +1/2=9/2`

`=>(x-3/2)^2=9/2-1/2`

`=>(x-3/2)^2= 8/2`

`=>(x-3/2)^2=4`

`=>(x-3/2)^2=(+-2)^2`

\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{3}{2}=4\\x-\dfrac{3}{2}=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4+\dfrac{3}{2}\\x=-4+\dfrac{3}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=-\dfrac{5}{2}\end{matrix}\right.\)

Vậy \(x\in\left\{\dfrac{11}{2};-\dfrac{5}{2}\right\}\)