Question

x²+1/x²=2. Then What is the value of 1/x ?
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Answer 1

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x+1/x=2

or, (x^2+1)/x =2

or, x^2+1=2x

or, x^2+1–2x=0

or, (x-1)^2=0

or, x-1=0

Therefore, x=1

Now, x^9+1/x^9

= 1^9+1/1^9

=1+1

=2

By applying this method you can also solve the similar types of questions, like

If x + 1/x =2, then what is the value of x^3 + 1/x^3 =?

If x + 1/x =2, then what is the value of x^5+ 1/x^5 =?

If x + 1/x =2, then what is the value of x^7 + 1/x^7 =?

etc. etc.

In each case, the answer will be 2