Question

If \( y = x + \frac{1}{x} \) then \( x^4 + x^3 - 4x^2 + x + 1 = \)

• A. \( x^2(y^2 + y - 2) \)
• B. \( x^2(y^2 + y - 3) \)
• C. \( x^2(y^2 + y - 4) \)
• D. \( x^2(y^2 + y - 6) \)

Hint:

In cases involving algebraic identities, carefully expand and substitute given equations to simplify the expressions.

Answer 1

The Correct Option is D

Given \( y = x + \frac{1}{x} \), we are asked to simplify the expression \( x^4 + x^3 - 4x^2 + x + 1 \). Start by expanding \( y = x + \frac{1}{x} \), and then manipulate the given expression by substituting \( y \) and simplifying it accordingly. Ultimately, the simplification leads to the answer \( x^2(y^2 + y - 6) \).