Correct Answer - Option 4 : 25

**Given:**

x(x - 5) = 7

⇒ x^{2} – 5x = 7

**Concept:**

Cube both side of the given equation and then proceed.

**Formula used:**

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

**Calculation:**

∵ x^{2} - 5x = 7

On cubing both sides, we get;

(x^{2} – 5x)^{3} = 7^{3}

⇒ x^{6} - 125x^{3} – [3 × (x^{2}) × 5x(x^{2} – 5x)] = 343

⇒ x^{6} - 125x^{3} - [3 × x^{2} × (5x) × (7)] = 343

⇒ x^{6} - 125x^{3} - 105x^{3} = 343

⇒ x^{6 }– 230x^{3} = 343 ------(1)

Putting the value of (1) in (x^{6} – 230x^{3} – 243)/4;

⇒ (343 – 243)/4

⇒ 100/4 = 25