Question

 \(\left(x-2\right)^2=1\)

\(\left(2x-1\right)^3=-8\)

\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)

Answer 1

\(\left(x-2\right)^2=1=>x-2=1=>\)\(x=3\)

\(\left(2x-1\right)^3=-8=>2x-1=-2\)\(=>2x=-2+1=-1\)\(=>x=-1:2=\frac{-1}{2}\)

\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}=>\left(x+\frac{1}{2}\right)=\frac{1}{8}\)\(=>x=\frac{1}{8}-\frac{1}{2}=>x=\frac{-6}{16}=\frac{-3}{8}\)

Answer 2

\(\left(x-2\right)^2=1\Rightarrow\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}.}\)

\(\left(2x-1\right)^3=-8\Rightarrow2x-1=-2\Rightarrow2x=-1\Rightarrow x=-\frac{1}{2}\)

\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\orbr{\begin{cases}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{cases}}\)

Answer 3

1) (x-2)^2=1^2

=) x-2=+1 hoặc x-2=-1

=)x=3                  x=1

2)(2x-1)^3=-8

=) (2x-1)^3=-2^3

=)2x-1=-2

=)x=-1/2

3)(x+1/2)^2=1/16

=)(x+1/2)^2=(1/4)^2

=) x+1/2=1/4 hoặc x+1/2=-1/4 

=)x= -1/4                    x=-3/4

Answer 4

a) \(\left(x-2\right)^2=1\Leftrightarrow\left(x-2\right)^2=1^2=\left(-1\right)^2\Rightarrow x-2=1\) hoặc \(-1\)

Xét \(x-2=1\Rightarrow x=3\)

\(x-2=-1\Rightarrow x=1\)

Vậy x = 1 hoặc -1

b) \(\left(2x-1\right)^3=-8\Leftrightarrow\left(2x-1\right)^3=\left(-2\right)^3\Rightarrow2x-1=-2\)

\(\Rightarrow2x=-1\Rightarrow x=-\frac{1}{2}\)

c) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\Leftrightarrow\left(x+\frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2=\left(-\frac{1}{4}\right)^2\Rightarrow x+\frac{1}{2}=\frac{1}{4}\) hoặc \(-\frac{1}{4}\)

Xét \(x+\frac{1}{2}=\frac{1}{4}\Rightarrow x=-\frac{1}{4}\)

\(x+\frac{1}{2}=-\frac{1}{4}\Rightarrow x=-\frac{3}{4}\)