Evaluate :

$\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}$

Substituting a = 5.67 and b = 4.33, we get :

$\Rightarrow \dfrac{a \times a \times a + b \times b \times b}{a \times a - a \times b + b \times b} \\[1em] \Rightarrow \dfrac{a^3 + b^3}{a^2 - ab + b^2} \\[1em] \Rightarrow \dfrac{(a + b)(a^2 - ab + b^2)}{a^2 - ab + b^2} \\[1em] \Rightarrow (a + b) \\[1em] \Rightarrow (5.67 + 4.33) \\[1em] \Rightarrow 10.$

Hence, $\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33} = 10$.