Question : The value of $\frac{1.6 \times 1.6 \times 1.6-0.6 \times 0.6 \times 0.6}{1.6 \times 1.6+1.6 \times 0.6+0.6 \times 0.6}$ is:
Option 1: 0
Option 2: 1
Option 3: –1
Option 4: 2
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Correct Answer: 1
Solution :
$\frac{1.6 \times 1.6 \times 1.6-0.6 \times 0.6 \times 0.6}{1.6 \times 1.6+1.6 \times 0.6+0.6 \times 0.6}$
$=\frac{(1.6)^3 - (0.6)^3}{1.6^2 + 1.6\times0.6 + 0.6^2}$
$=\frac{(1.6 - 0.6)(1.6^2 + 1.6\times0.6 + 0.6^2)}{1.6^2 + 1.6\times0.6 + 0.6^2}$
$=1.6-0.6 = 1$
Hence, the correct answer is 1.
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