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If a + a2 + a3 - 1 = 0, then what is the value of $${a^3} + \frac{1}{a}?$$
Answer & Solution
Correct Answer:
Option
C
a + a2 + a3 - 1 = 0
a3 = 1 - a2 - a . . . . . . . . (i)
a + a2 + a3 = 1
on dividing by a
a2 + a + 1 = $$\frac{1}{a}$$ . . . . . . . . (ii)
Add equation (i) & (ii),
$${a^3} + \frac{1}{a}$$
= 1 - a2 - a + a2 + a + 1
= 2
a3 = 1 - a2 - a . . . . . . . . (i)
a + a2 + a3 = 1
on dividing by a
a2 + a + 1 = $$\frac{1}{a}$$ . . . . . . . . (ii)
Add equation (i) & (ii),
$${a^3} + \frac{1}{a}$$
= 1 - a2 - a + a2 + a + 1
= 2
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