If K + \({{1} \over K}\) + 2 = 0 and K < 0, then what is the value of K¹⁰ + \({{1} \over K^{11}}\)?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 2)

Answer 1

Given:

K + \({{1} \over K}\) + 2 = 0

Formula Used:

The concept of quadratic equation is used

Calculations:

As from given part

⇒ K + \({{1} \over K}\) + 2 = 0

⇒ \((\sqrt K + \frac{1}{\sqrt k})^2 = 0\)

⇒ \((\sqrt K + \frac{1}{\sqrt k}) = 0\)

⇒ \(\sqrt K = - \frac{1}{\sqrt k}\)

⇒ K = -1

Now, According to the question,

⇒ K10 + \({{1} \over K^{11}}\) = (-1)¹⁰ + \({{1} \over (-1)^{11}}\) = 1+ \({{1} \over (-1)}\) = 1 - 1 = 0

⇒ Hence, The value of the above equation is 0