- 5√8
- 5√6
- 8√3
- 8√5

Option 4 : 8√5

**Given:**

x87 - 1/x87 = 4

**Formula used:**

If x - 1/x = k, then x + 1/x = √(k^{2} + 4)

a^{2} - b^{2} = (a + b)(a - b)

**Calculation:**

x87 + 1/x87 = √(4^{2} + 4)

⇒ √20

⇒ 2√5

Now, x174 - 1/x174 = (x87)^{2} - (1/x87)^{2}

⇒ (x87 + 1/x87 )(x87 - 1/x87)

⇒ 2√5 × 4

⇒ 8√5

**∴ The value of x174 - 1/x174 is 8√5.**

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