Question

(4.75 x 4.75 x 4.75 + 1.25 x 1.25 x 1.25) / ( 4.75 x 4.75 + 1.25 x 1.25 - 4.75 x 1.25) = ?

Answer 1

$$\begin{gathered} \frac{4.75\times 4.75\times 4.75+1.25\times 1.25\times 1.25}{4.75\times 4.75+1.25\times 1.25-4.75\times 1.25} \\ =\frac{{\left(4.75\right)}^3+{\left(1.25\right)}^3}{{\left(4.75\right)}^2+{\left(1.25\right)}^2-4.75\times 1.25} \\ =\frac{\left(4.75+1.25\right)\left[{\left(4.75\right)}^2+{\left(1.25\right)}^2-4.75\times 1.25\right]}{\left[{\left(4.75\right)}^2+{\left(1.25\right)}^2-4.75\times 1.25\right]}\left[\mathbf{Using}\mathbf{}\mathbf{identity}\mathbf{}\mathbf{:}\mathbf{}{\mathbf{a}}^{\mathbf{3}}\mathbf{+}{\mathbf{b}}^{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\left({\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\mathbf{-}\mathbf{ab}\right)\right] \\ =\left(4.75+1.25\right) \\ =6 \end{gathered}$$