$\frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} = ?$ $\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} = ?$

10.27
20.4087
30.73
41

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ \frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} \\ let a = 0.73 and b = 0.27 \\ = \frac{(0.73 + 0.27) [{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27]}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} \\ [∵ a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)] \\ = 0.73 + 0.27 \\ = 1 \end{aligned}

$\eqalign{ & {\text{Given,}} \cr & \frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} \cr & {\text{let }}a = 0.73{\text{ and }}b = 0.27 \cr & = \frac{{\left( {0.73 + 0.27} \right)\left[ {{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27} \right]}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} \cr & \left[ {\because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)} \right] \cr & = 0.73 + 0.27 \cr & = 1 \cr}$