Correct Answer - Option 2 : 8
Given:
x3 – 5x2 + 17 = 4(x – 1)
Calculations:
x3 – 5x2 + 17 = 4(x – 1)
⇒ x3 – 5x2 + 1 = 4x – 4 – 16
⇒ x2 (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.