The value of [ (5.169 × 5.169 × 5.169) + 64 × (0.888)³ ] ÷ [ (5.169)² +…
2020
The value of [ (5.169 × 5.169 × 5.169) + 64 × (0.888)³ ] ÷ [ (5.169)² + (3.552)² − 4 × (0.888) × (5.169) ] is (8 + k). Find the value of k.
- A.
0.388
- B.
0.656
- C.
0.721
- D.
0.129
Attempted by 9 students.
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Correct answer: C
Let a = 5.169 and b = 3.552. Notice that b = 3.552 = 4 × 0.888, so 64 × (0.888)³ = (4 × 0.888)³ = (3.552)³ = b³.
Numerator = (5.169)³ + 64 × (0.888)³ = a³ + b³.
Denominator = (5.169)² + (3.552)² − 4 × (0.888) × (5.169) = a² + b² − ab (since 4 × 0.888 × 5.169 = 3.552 × 5.169 = ab).
Use the identity a³ + b³ = (a + b)(a² − ab + b²). Therefore (a³ + b³) ÷ (a² − ab + b²) = a + b.
So the expression = a + b = 5.169 + 3.552 = 8.721.
Given the value equals (8 + k), we have 8 + k = 8.721, hence k = 0.721.