Question

if x+1/x= -2 then x to the power 2017+1/x to the power 2017=?
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Answer 1

-2

Step-by-step explanation:

Given:

$x + \dfrac{1}{x} = - 2$

To Find:

$\sf \: The \: value \: of \: \: {x}^{2017} + \dfrac{1}{ {x}^{2017} }$

How I will get answer ?

1. Solve The given

2. Get the value of x

3. Put the value of x in question

4. Simplify till answer

Solution:

$x + \dfrac{1}{x} = - 2$

$\dfrac{ {x}^{2} + 1 }{x} = - 2$

${x}^{2} + 1 = - 2x$

${x}^{2} + 2x + 1 = 0$

${(x + 1)}^{2} = 0$

$x + 1 = 0$

$x = - 1$

Hence, The value of x is -1

Now,

1) If the power will odd then value will remain in -ve.

2)If the power will even then value will change in +ve.

As, 2017 is a odd no.

So,

${x}^{2017} + \dfrac{1}{ {x}^{2017} }$

$= { (- 1)}^{2017} + \dfrac{1}{ {( - 1)}^{2017} }$

$= - 1 + \dfrac{1}{ - 1}$

$= - 1 - 1$

$= - 2$

Therefore, The required answer is -2 .