Question : If $x + \frac{1}{x} = - 2$ , then what is the value of $x^{17} + x^{- 17} + x^{12} + x^{- 12} ? (x < 0)$
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 0

Question

Question : If $(x + \frac{1}{x}) = - 2$ , then the value of $(x^{7} + \frac{1}{x^{7}})$ is:

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Answer 1

Correct Answer: 0

Solution : Given $x + \frac{1}{x} = - 2$
$\Rightarrow x^{2} + 1 = - 2 x$
$\Rightarrow x^{2} + 2 x + 1 = 0$
$\Rightarrow (x + 1)^{2} = 0$
$\Rightarrow x = - 1$
Now, putting the value of $x = - 1$ in $x^{17} + x^{- 17} + x^{12} + x^{- 12}$ we get:
$= (- 1)^{17} + (- 1)^{- 17} + (- 1)^{12} + (- 1)^{- 12}$
$= - 1 - 1 + 1 + 1 = 0$
Hence, the correct answer is 0.

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Question : If x+1x=−2, then what is the value of x17+x−17+x12+x−12?(x<0)Option 1: –2Option 2: –1Option 3: 1Option 4: 0

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Question : If $x + \frac{1}{x} = - 2$ , then what is the value of $x^{17} + x^{- 17} + x^{12} + x^{- 12} ? (x < 0)$
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 0