Question : The value of $\frac{5.35 \times 5.35 \times 5.35+3.65 \times 3.65 \times 3.65}{53.5 \times 53.5+36.5 \times 36.5-53.5 \times 36.5}$ is:
Option 1: 0.09
Option 2: 0.9
Option 3: 90
Option 4: 9
Correct Answer: 0.09
Solution :
Given: $\frac{5.35 \times 5.35 \times 5.35+3.65 \times 3.65 \times 3.65}{53.5 \times 53.5+36.5 \times 36.5-53.5 \times 36.5}$
= $\frac{(5.35)^3+(3.65)^3}{(53.5)^2+(36.5)^2-53.5 \times 36.5}$
= $\frac{(5.35+3.65)((5.35)^2+(3.65)^2-5.35 \times 3.65)}{100\times[(5.35)^2+(3.65)^2-5.35 \times 3.65]}$
= $\frac{5.35+3.65}{100}$
= $\frac{9}{100}$
= 0.09
Hence, the correct answer is 0.09.
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