Question

If (x+1/x) ²=3, show that (x³+1/x³) =0​

Answer 1

Given:

★ (x + 1/x)² = 3

To prove:

☞ (x³ + 1/x³) = 0

Identity used:

• (a + b)³ = a³ + b³ + 3ab(a + b)

Method:

According to the question,

x + 1/x = √3

(x + 1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)

Substitute x + 1/x as √3

→ √3³ = x³ + 1/x³ + 3(√3)

→ 3√3 = x³ + 1/x³ + 3√3

→ 3√3 - 3√3 = x³ + 1/x³

→ x³ + 1/x³ = 0

Hence proved