Question : If $x+\frac{1}{x}=-2$, then the value of $x^p +x^q$ is: (where $p$ is an even number and $q$ is an odd number)
Option 1: –2
Option 2: 2
Option 3: 1
Option 4: 0
Answer (1)
14th Jan, 2024
Correct Answer: 0
Solution :
Given: $x+\frac{1}{x}=-2$
$x^2 + 1 = -2x$
⇒ $x^2 + 2x + 1 = 0$
⇒ $(x+1)^2 = 0$
⇒ $x = -1$
Given expression,
$x^p + x^q$, where p is even and q is odd,
$(-1)^{even} = 1$ and $(-1)^{odd} = -1$
$\therefore$ The expression becomes 1 + (–1) = 0
Hence, the correct answer is 0.
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