Question

Write the value of ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3$

Answer 1

${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^{3}Leta=\frac{1}{2},b=\frac{1}{3}andc=\frac{-5}{6}\because a+b+c=\frac{1}{2}+\frac{1}{3}-\frac{5}{6}=\frac{3+2-5}{6}=\frac{0}{6}=0a^3+b^3+c^3=3abc\therefore {\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-\left(\frac{-5}{6}\right)=3\times \frac{1}{2}\times \frac{1}{3}\times \left(\frac{-5}{6}\right)=\frac{-5}{12}$