Question

if (x+1/x)^2 =3, then find x3+1/x3. plz give relevant answers. ​

Answer 1

Given :

• (x + 1/x)² = 3

To find :

• x³ + 1/x³

SoIution :

Let's start with what's given :

⇒ (x + 1/x)² = 3

⇒ x + 1/x = √3  ····················· (i)

Now we know the identity :

⇔ a³ + b³ = (a + b)³ - 3(a + b)

Taking a = x and b = 1/x :

⇒ x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

Putting vaIues from (i) :

⇒ x³ + 1/x³ = (√3)³ - 3√3

⇒ x³ + 1/x³ = (√3)² × √3 - 3√3

⇒ x³ + 1/x³ = 3√3 - 3√3

⇒ x³ + 1/x³ = 0

∴ Required vaIue of x³ + 1/x³ = 0

Answer 2

Answer:

Hope it's helpful to you.