Question : If $a-b=8$ and $4ab=84$, then what is the value of $3a^3-3b^3$?
Option 1: 1016
Option 2: 2032
Option 3: 1018
Option 4: 3048
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Correct Answer: 3048
Solution :
Given: $a-b=8$ and $4ab=84$
⇒ $ab=21$
Now, $a-b=8$
Cubing both sides we get,
⇒ $(a-b)^3=8^3$
⇒ $a^3-b^3-3ab(a-b)=512$
Putting the values, we get:
⇒ $a^3-b^3-3\times 21\times8=512$
⇒ $a^3-b^3=512+504$
⇒ $a^3-b^3=1016$
$\therefore 3a^3-3b^3 =3\times1016=3048$
Hence, the correct answer is 3048.
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