Question
If $a - b = 4$ and $ab = 21,$ find the value of $a^3 - b^3.$
✓
Answer
In the given problem, we have to find the value of $a^3 - b^3$
Given $a - b = 4, ab = 21$
We shall use the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
Here putting $a - b = 4, ab = 21,$
$\Rightarrow (4)^3 = a^3 - b^3 + 3(21)(4)$
$\Rightarrow 64 = a^3 - b^3 - 252$
$\Rightarrow 64 – 252 = a^3 - b^3$
$\Rightarrow 316 = a^{3 }- b^3$
Hence, the value of $a^{3 }- b^3$ is $316.$
Given $a - b = 4, ab = 21$
We shall use the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
Here putting $a - b = 4, ab = 21,$
$\Rightarrow (4)^3 = a^3 - b^3 + 3(21)(4)$
$\Rightarrow 64 = a^3 - b^3 - 252$
$\Rightarrow 64 – 252 = a^3 - b^3$
$\Rightarrow 316 = a^{3 }- b^3$
Hence, the value of $a^{3 }- b^3$ is $316.$
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