Question

(a+1/a) (a^3+1/a^3)
Answer it in step by step​

Answer 1

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

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