Question : If $a-b = 5$ and $ab = 24$, find the value of $a^3-b^3$.
Option 1: 455
Option 2: 485
Option 3: 385
Option 4: 360
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Correct Answer: 485
Solution :
Given: $a-b = 5$ and $ab = 24$
$(a-b)^3=5^3$
$⇒a^3 - b^3 - 3ab(a-b) = 125$
$⇒a^3 - b^3 = 125 + (3×24×5) = 125 + 360 = 485$
Hence, the correct answer is 485.
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