​$$\frac{(2.3)^3 + (0.3)^3}{(2.3)^2 - 0.69 + (0.3)^2}$$​ has the value-

Correct option is C

Given:

​$$\frac{(2.3)^3 + (0.3)^3}{(2.3)^2 - 0.69 + (0.3)^2}$$​​

Concept Used:

$$\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\\hline \text{Brackets} &[],{}, () \\ \hline \text{Orders, of} & (power), √ (root) , of \\ \hline \text{Division}& ÷ \\ \hline \text{Multiplication} & × \\ \hline \text{Addition} & + \\ \hline \text{Subtraction} & - \\\hline \end{array}$$​​

Formula Used:

​$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$​​

Solution:

$$\frac{(2.3)^3 + (0.3)^3}{(2.3)^2 - 0.69 + (0.3)^2}$$

Let a = 2.3, b = 0.3

= $$\frac{(2.3 + 0.3)((2.3)^2 - (2.3)(0.3) + (0.3)^2)}{ {(2.3)^2 - 0.69 + (0.3)^2}}$$​

= $$\frac{(2.3 + 0.3)((2.3)^2 - 0.69 + (0.3)^2)}{ {(2.3)^2 - 0.69 + (0.3)^2}}$$

= (2.3 + 0.3)

= 2.6

Thus, the correct answer is (c).