Correct Answer - Option 2 : 8

**Given:**

x3 – 5x2 + 17 = 4(x – 1)

**Calculations:**

x^{3} – 5x^{2} + 17 = 4(x – 1)

⇒ x^{3} – 5x^{2} + 1 = 4x – 4 – 16

⇒ x^{2} (x – 5) + 1 = 4x – 20

⇒ x2 (x – 5) + 1 = 4(x – 5)

\(\Rightarrow [x{^2}\ \times \ \frac{x\ -\ 5}{x\ -\ 5}\ +\ \frac{1}{x\ -\ 5}] = 4\)

\(\Rightarrow [x{^2}\ +\ \frac{1}{x\ -\ 5}] = 4\)

\(\Rightarrow 2[x{^2}\ +\ \frac{1}{x\ -\ 5}] = 8\)

**∴ The value of \(2[x{^2}\ +\ \frac{1}{x\ -\ 5}]\) is 8.**