Question : What is the value of 1.65 × 1.65 × 1.65 + 0.35 × 0.35 × 0.35 + 3.465?
Option 1: 8
Option 2: 7.5
Option 3: 4
Option 4: 5.5
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Correct Answer: 8
Solution : 1.65 × 1.65 × 1.65 + 0.35 × 0.35 × 0.35 + 3.465 = (1.65) 3 + (0.35) 3 + 3 × 1.65 × 0.35 × (1.65 + 0.35) Using $(a + b)^3 = a^3+b^3 + 3ab (a+b)$ = (1.65 + 0.35) 3 = 2 3 = 8 Hence, the correct answer is 8.
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