If, a + b = 24 and a² + b² = 320, then find the value of (a³ + b³).
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Correct answer: A
Explanation
Given:
a + b = 24
a² + b² = 320
By the formula:
a² + b² = (a + b)² − 2ab
a³ + b³ = (a + b)³ − 3ab(a + b)
320 = 24² − 2ab
320 = 576 − 2ab
2ab = 256
ab = 128
a³ + b³ = 24³ − 3 × 128 × 24
= 13824 − 9216 = 4608