If a + a2 + a3 - 1 = 0 then...

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If a + a² + a³ - 1 = 0, then what is the value of $${a^3} + \frac{1}{a}?$$

A. 1

B. 4

C. 2

D. 3

Answer: Option C

Solution (By Examveda Team)

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

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If a + a2 + a3 - 1 = 0 then...

If a + a2 + a3 - 1 = 0, then what is the value of $${a^3} + \frac{1}{a}?$$

Solution (By Examveda Team)

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If a + a² + a³ - 1 = 0, then what is the value of $${a^3} + \frac{1}{a}?$$