If #a^3 + 3a^2 + 9a = 1#, then what is the value of #a^3 + (3/a)#?

1 Answer
MattyMatty
May 4, 2018

#28#

Explanation:

#a^3 + 3 a^2 + 9 a + 27 " has root "a = -3.#
#"So we divide away the factor "(a + 3) : #
#a^3 + 3 a^2 + 9 a + 27 = (a + 3)(a^2+9) = 28#

#"Now we try to solve "(a+3)(a^2+9) = 28.#
#"We multiply both sides with "(a-3) : "#

#(a+3)(a-3)(a^2+9) = 28(a-3)#
#=> (a^2-9)(a^2+9) = 28(a-3)#
#=> (a^4 - 81) = 28(a - 3)#
#=> a^4 - 28 a + 3 = 0#

#"Now we divide both sides by a : "#

#=> a^3 + 3/a = 28#

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