If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a) ?
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Correct answer: C
Explanation
The correct answer is option 3 ie 28.
a³ + 3a² + 9a = 1
a(a² + 3a +9) = 1
a² + 3a +9 = 1/a
a³ - b³ = (a - b)(a² + ab + b²)
for b = 3
a³ - 3³ = (a - 3)(a² + 3a + 9)
a³ - 27 = (a - 3)(1/a)
a³ + (3/a) = 1 + 27
a³ + (3/a) = 28