Question
If a3 + 3a2 + 9a = 1, then what
is the value of a3 + (3/a)?Solution
a3 + 3a2 + 9a = 1 a(a2 + 3a + 9) = 1 a2 + 3a + 9 = 1/a (a3 – b3) = (a − b)(a2 + ab + b2) for b=3 we have (a3 – 33) = (a – 3)(a2 +3a +9) (a3 − 27)=(a − 3)(1/a) a3 + (3/a) = 1 + 27 a3 + (3/a) = 28
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