Question

Prove that $\frac{59\times 59\times 59-9\times 9\times 9}{59\times 59+59\times 9+9\times 9}=50$.

Answer 1

$$\begin{gathered} \frac{59\times 59\times 59-9\times 9\times 9}{59\times 59+59\times 9+9\times 9} \\ =\frac{{\left(59\right)}^3-9^3}{{59}^2+59\times 9+9^2} \end{gathered}$$
$$\begin{gathered} \mathrm{We}\mathrm{know} \\ {a}^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right) \\ \mathrm{Here}a=59,b=9 \\ \mathrm{So},\frac{\left(59-9\right)\left({59}^2+9^2+59\times 9\right)}{{59}^2+9^2+59\times 9}=59-9=50:\mathrm{RHS} \end{gathered}$$
Thus, LHS=RHS