Question : Simplify the following expression. $\frac{(0.96 \times 0.96 \times 0.96+0.04 \times 0.04 \times 0.04)}{(0.96 \times 0.96-0.96 \times 0.04+0.04 \times 0.04)}$
Option 1: 0
Option 2: 0.82
Option 3: 2
Option 4: 1
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Correct Answer: 1
Solution :
According to the question,
$\frac{(0.96 \times 0.96 \times 0.96+0.04 \times 0.04 \times 0.04)}{(0.96 \times 0.96-0.96 \times 0.04+0.04 \times 0.04)}$
Let $0.96=a, 0.04=b$
So, the equation = $\frac{a^3+b^3}{a^2-ab+b^2}=\frac{(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}=(a+b)$
Putting the value of $a,b$, we get $(0.96+0.04)=1$
Hence, the correct answer is 1.
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