Option 3 : 18

**Given:**

The given equation is

x + (1/x) = 3

**Concept used:**

As we know,

x^{-1} = 1/x

**Formula used:**

Using this identity

(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)

**Calculations:**

According to the question, we have

(a + b)3 = a3 + b3 + 3ab(a + b) ----(1)

Put the value of a = x and b = 1/x in equation (1), we get

⇒ {(x + (1/x)}3 = x3 + (1/x)3 + 3(x)(1/x){x + (1/x)}

⇒ {(x + (1/x)}3 = x3 + (1/x^{3}) + 3{x + (1/x)}

⇒ (3)^{3} = x3 + (1/x3) + 3(3)

⇒ x3 + (1/x3) = 27 - 9

⇒ x3 + (1/x3) = 18

⇒ x3 + x-3 = 18

**∴ The value of x3 + x-3 is 18.**

Use this formula to solve this type of questions

If x + (1/x) = p then x3 + (1/x3) = p3 - 3p

So, the value of p = 3

then, the value of x3 + (1/x3) is

⇒ x3 + (1/x3) = (3)3 - 3(3)

⇒ x3 + (1/x3) = 18

∴ The value of x3 + x-3 is 18.