Question

(1/2+1/3).(x-1/4)^2+(3/2-1/2).(x-1/4)^2=8

 

Answer 1

\(\Leftrightarrow\left(x-\dfrac{1}{4}\right)^2\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{3}{2}-\dfrac{1}{2}\right)=8\)

\(\Leftrightarrow\left(x-\dfrac{1}{4}\right)^2=8:\dfrac{13}{6}=\dfrac{48}{13}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{4}=\sqrt{\dfrac{48}{13}}\\x-\dfrac{1}{4}=-\sqrt{\dfrac{48}{13}}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{48}{13}}+\dfrac{1}{4}\\x=-\sqrt{\dfrac{48}{13}}+\dfrac{1}{4}\end{matrix}\right.\)