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1. Simplify : $\frac{0.41 \times 0.41 \times 0.41 + 0.69 \times 0.69 \times 0.69}{0.41 \times 0.41 - 0.41 \times 0.69 + 0.69 \times 0.69} = ?$

A. 0.28

B. 1.41

C. 1.1

D. 2.8

Solution:

\begin{aligned} \frac{0.41 \times 0.41 \times 0.41 + 0.69 \times 0.69 \times 0.69}{0.41 \times 0.41 - 0.41 \times 0.69 + 0.69 \times 0.69} \\ = \frac{{(0.41)}^{3} + {(0.69)}^{3}}{{(0.41)}^{2} - 0.41 \times 0.69 + {(0.69)}^{2}} \\ . . . . . [∵ a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)] \\ = 0.41 + 0.69 \\ = 1.1 \end{aligned}

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