Question : The value of $\frac{4.35×4.35×4.35+3.25×3.25×3.25}{43.5×43.5+32.5×32.5-43.5×32.5}$ is:
Option 1: 0.0076
Option 2: 0.76
Option 3: 0.076
Option 4: 7.6
Correct Answer: 0.076
Solution :
Given: $\frac{4.35×4.35×4.35+3.25×3.25×3.25}{43.5×43.5+32.5×32.5-43.5×32.5}$
= $\frac{(4.35^{3}) + ( 3.25)^{3}}{43.5^{2} + 32.5^{2} - 43.5 × 32.4}$
= $\frac{(4.35 + 3.25)(4.35^{2} + 3.25^{2} - 4.35 × 3.25)}{100×(4.35^{2} + 3.25^{2} - 4.35 × 3.25)}$
= $\frac{4.35 + 3.25}{100}$
= $\frac{7.6}{100}$
= 0.076
Hence, the correct answer is 0.076.
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