​ Write the value of: (1/2)^3 + (1/3)^3 - (5/6)^3

Question

Write the value of:

\((\frac{1}{2})^{3}+\,(\frac{1}{3})^{3}\,-(\frac{5}{6})^{3}\)

Answer 1

We have ,

\(=(\frac{1}{2})^{3}+(\frac{1}{3})^{3}-(\frac{5}{6})^{3}\,given\)

Let a = \(\frac{1}{2},\,b=\frac{1}{3},c=-\frac{5}{6},\) 

then the expression becomes

\(=(\frac{1}{2})^{3}+(\frac{1}{3})^{3}-(\frac{5}{6})^{3}=a^{3}+b^{3}+c^{3}\)

Here,

\(=a+b+c=\frac{1}{2}+\frac{1}{3}-\frac{5}{6}=0\)

Hence ,