Question

if a+1÷a=pand ais not equal to 0show that a^31÷a^3=p(p^2-3)

Answer 1

Hope u like my process
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HERE WE GO,

a + 1/a = p

Cubing both sides we get,
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
( a +1/a)³ = p³

or, a³ +1/a³ +3a.1/a(a +1/a) =p³

__[since (a +b) ³ = a³ + b³ +3ab(a+b)]__

or, a³ + 1/a³ +3p = p³ _(since a +1/a =p) _

or, a³ + 1/a³ = p³ - 3p

or, a³ +1/a³ = p(p² - 3) ___[ proved] ___
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Hope this is ur required answer.

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