Question

Answer 1

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

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-2\right)^3\)

\(\Rightarrow x-\dfrac{1}{2}=-2\)

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

\(\Rightarrow x=-\dfrac{3}{2}\)

2) \(\left(x-\dfrac{1}{2}\right)^3=\dfrac{27}{8}\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(\dfrac{3}{2}\right)^3\)

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

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

\(\Rightarrow x=2\)

3) \(\left(x-\dfrac{1}{3}\right)^3=\dfrac{-8}{27}\)

\(\Rightarrow\left(x-\dfrac{1}{3}\right)^3=\left(\dfrac{-2}{3}\right)^3\)

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

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

\(\Rightarrow x=-\dfrac{1}{3}\)

4) \(\left(x-\dfrac{1}{3}\right)^3=\dfrac{8}{27}\)

\(\Rightarrow\left(x-\dfrac{1}{3}\right)^3=\left(\dfrac{2}{3}\right)^3\)

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

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

\(\Rightarrow x=1\)

5) \(\left(x-\dfrac{5}{2}\right)^3=-\dfrac{1}{8}\)

\(\Rightarrow\left(x-\dfrac{5}{2}\right)^3=\left(-\dfrac{1}{2}\right)^3\)

\(\Rightarrow x-\dfrac{5}{2}=-\dfrac{1}{2}\)

\(\Rightarrow x=-\dfrac{1}{2}+\dfrac{5}{2}\)

\(\Rightarrow x=2\)

6) \(\left(x-\dfrac{1}{8}\right)^3=\dfrac{-8}{125}\)

\(\Rightarrow\left(x-\dfrac{1}{8}\right)=\left(\dfrac{-2}{5}\right)^3\)

\(\Rightarrow x-\dfrac{1}{8}=\dfrac{-2}{5}\)

\(\Rightarrow x=-\dfrac{2}{5}+\dfrac{1}{8}\)

\(\Rightarrow x=-\dfrac{11}{40}\)