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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

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{{0.41 \times 0.41 \times 0.41 + 0.69 \times 0.69 \times 0.69}}{{0.41 \times 0.41 - 0.41 \times 0.69 + 0.69 \times 0.69}} \cr & = \frac{{{{\left( {0.41} \right)}^3} + {{\left( {0.69} \right)}^3}}}{{{{\left( {0.41} \right)}^2} - 0.41 \times 0.69 + {{\left( {0.69} \right)}^2}}} \cr & .....\left[ {\because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)} \right] \cr & = 0.41 + 0.69 \cr & = 1.1 \cr} $$

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