Mathematics
If a - b = 7 and a2 + b2 = 85, then find the value of a3 - b3.
Expansions
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Answer
We know that,
⇒ (a - b)2 = a2 + b2 - 2ab
⇒ (7)2 = 85 - 2ab
⇒ 49 = 85 - 2ab
⇒ 2ab = 85 - 49
⇒ 2ab = 36
⇒ ab = 18.
We know that,
a3 - b3 = (a - b)(a2 + b2 + ab)
Substituting values we get,
⇒ a3 - b3 = 7(85 + 18) = 7(103) = 721.
Hence, a3 - b3 = 721.
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