Question

\(\left(x-\frac{1}{2}\right)^4=\left(x-\frac{1}{2}\right)^2\)

Giúp mk vs

Answer 1

\(\left(x-\frac{1}{2}\right)^4=\left(x-\frac{1}{2}\right)^2\)

<=> \(\left(x-\frac{1}{2}\right)^4-\left(x-\frac{1}{2}\right)^2=0\)

<=> \(\left(x-\frac{1}{2}\right)^2\left[\left(x-\frac{1}{2}\right)^2-1\right]=0\)

<=> \(\left[\begin{array}{nghiempt}\left(x-\frac{1}{2}\right)^2=0\\\left(x-\frac{1}{2}\right)^2-1=0\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x=\frac{1}{2}\\\left[\begin{array}{nghiempt}x-\frac{1}{2}=1\\x-\frac{1}{2}=-1\end{array}\right.\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x=\frac{1}{2}\\\left[\begin{array}{nghiempt}x=\frac{3}{2}\\x=-\frac{1}{2}\end{array}\right.\end{array}\right.\)

Vậy x \(\in\left\{\frac{1}{2};\frac{3}{2};-\frac{1}{2}\right\}\)