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If x3 – 5x2 + 17 = 4(x – 1), then what is the value of \(2[x{^2}\ +\ \frac{1}{x\ -\ 5}]\)?
1. 12
2. 8
3. 18
4. 15

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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.

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