Mathematics
If a - b = 3 and ab = 10, find: a3 - b3.
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Answer
Using the formula,
[∵ (x - y)3 = x3 - y3 - 3xy(x - y)]
So,
(a - b)3 = a3 - b3 - 3ab(a - b)
Putting the values a - b = 3 and ab = 10, we get
⇒ (3)3 = a3 - b3 - 3 x 10 x 3
⇒ 27 = a3 + b3 - 90
⇒ a3 + b3 = 27 + 90
⇒ a3 + b3 = 117
Hence, the value of a3 + b3 is 117.
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