Using suitable identity, find the value of :

$\dfrac{86 \times 86 \times 86 + 14 \times 14 \times 14}{86 \times 86 - 86 \times 14 + 14 \times 14}$

Let x = 86 and y = 14.

Hence, above equation can be written as,

$\Rightarrow \dfrac{x^3 + y^3}{x^2 - xy + y^2} \\[1em] = \dfrac{(x + y)(x^2 - xy + y^2)}{(x^2 - xy + y^2)} \\[1em] = x + y \\[1em] = 86 + 14 \\[1em] = 100.$

Hence, value of $\dfrac{86 \times 86 \times 86 + 14 \times 14 \times 14}{86 \times 86 - 86 \times 14 + 14 \times 14}$ = 100.