NIMCET 2009 — Mathematics PYQ

1. Simplify the Equation

Given the equation:

Since $x=0$ is not a root, we can divide the entire equation by $x^2$:

2. Group Similar Terms

Rearrange the terms to group those with the same coefficients:

3. Use Substitution

Let $t=x+\frac{1}{x}$.

Squaring both sides gives:

Therefore, $x^2+\frac{1}{x^2}=t^2-2$.

4. Form a Quadratic Equation in $t$

Substitute these into the grouped equation:

5. Solve for $t$

We can solve this quadratic equation using the factoring method:

Setting each factor to zero:

• $2t-5=0⟹t=\frac{5}{2}$

• $t+3=0⟹t=-3$

Conclusion:

The values of $x+\frac{1}{x}$ are $-3$ and $\frac{5}{2}$.

Final Answer:

The correct option is (a) $-3,\frac{5}{2}$.