Question

a+1/a=-√3,a³+1/a³=?​

Answer 1

Answer:

0

Step-by-step explanation:

We need to find a² + 1/a² in order to find a³ + 1/a³

a + 1/a = - √3

Squaring both the sides,

(a + 1/a)² = (-√3)²

=> a² + 1/a² + 2 = 3

=> a² + 1/a²= 3 - 2

=> a² + 1/a² = 1

Now, we know that,

a³ + b³ = (a + b)(a² + b² - ab)

Here a = a and b = 1/a

so, a³ + 1/a³ = (a + 1/a)[a² + 1/a² - a(1/a)]

a³ + 1/a³ = (-√3)(1 - 1)

(since, a + 1/a = -√3, a × 1/a = 1 and a² + 1/a² = 1 as derived above)

=> a³ + 1/a³ = (-√3)(0)

=> a³ + 1/a³ = 0