\(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)
<=>\(x-\frac{1}{2}=\frac{1}{3}\)
\(x=\frac{1}{3}+\frac{1}{2}=\frac{5}{6}\)
b)
\(\left(x-\frac{1}{2}\right)^2=\frac{4}{25}\)
\(\orbr{\begin{cases}x-\frac{1}{2}=\frac{2}{5}\\x-\frac{1}{2}=-\frac{2}{5}\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{2}{5}+\frac{1}{2}=\frac{9}{10}\\x=-\frac{2}{5}+\frac{1}{2}=\frac{1}{10}\end{cases}}\)
a)(x-1/2)3=1/27
x-1/2=1/3
x=5/6
b)(x-1/2)2=4/25
x-1/2=2/5
x=9/10
a) \(\left(\frac{x-1}{2}\right)^3=\frac{1}{27}\)
\(\left(\frac{x-1}{2}\right)^3=\frac{1}{3}^3\)
\(\Rightarrow\frac{x-1}{2}=\frac{1}{3}\)
\(\Rightarrow\left(x-1\right).3=2.1\)
\(\Rightarrow\left(x-1\right).3=2\)
\(\Rightarrow x-1=\frac{2}{3}\)
\(\Rightarrow x=\frac{2}{3}+1\)
\(\Rightarrow x=\frac{5}{3}\)
b) \(\left(\frac{x-1}{2}\right)^2=\frac{4}{25}\)
\(\left(\frac{x-1}{2}\right)^2=\frac{2}{5}^2\)
\(\Rightarrow\frac{x-1}{2}=\frac{2}{5}\)
\(\Rightarrow\left(x-1\right).5=2.2\)
\(\left(x-1\right).5=4\)
\(\Rightarrow x-1=\frac{4}{5}\)
\(\Rightarrow x=\frac{4}{5}+1\)
\(\Rightarrow x=\frac{9}{5}\)
