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A + 1/a= p find a^3 + 1/a^3

(1) p^3 + 3p

(2) 3p

(3) p^3 - 3p



User OnCompletion
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1 Answer

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23 votes

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Answer:

(3) p^3 -3p

Explanation:

(a +1/a) = p . . . . . . . given

(a +1/a)^3 = p^3 . . . . . . . . cube both sides

a^3 +3a^2(1/a) +3a(1/a)^2 +(1/a)^3 = p^3 . . . . . . expand

(a^3 +1/a^3) +3(a +1/a) = p^3 . . . . . . . . . . simplify, group

(a^3 +1/a^3) +3p = p^3 . . . . . . . . . . substitute p for a+1/a

(a^3 +1/a^3) = p^3 -3p . . . . . . subtract 3p from both sides

User Vincent L
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