- 263
- 375
- 363
- 275

Option 3 : 363

**Given:**

x2 + 1 = 7x

**Concept used:**

If (x + 1/x = a), then

x^{2} + 1/x^{2} = a^{2} - 2

x^{3} + 1/x^{3} = a^{3} - 3a

**Calculation:**

x2 + 1 = 7x

Divide the above term by x.

x + 1/x = 7

x^{3} + 1/x^{3} = (7)^{3} - 3 × 7

⇒ x3 + 1/x3 = 322 ----(1)

Similarly, x2 + 1/x2 = (7)2 - 2

⇒ x2 + 1/x2 = 47 ----(2)

Now, (x6 + x5 - 6x3 + x + 1)/x^{3}

⇒ (x3 + 1/x3) + (x2 + 1/x2) - 6

Putting the values of equation (1) and (2) in (x3 + 1/x3) + (x2 + 1/x2) - 6, we get

⇒ 322 + 47 - 6

⇒ 363

**∴ The required value is 363.**

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