Question

please solve this question

Answer 1

Given Equation is (x + 1/x)^2 = 3.

We know that (a + b)^2 = a^2 + b^2 + 2ab.

x^2 + 1/x^2 + 2 * x^2 * 1/x^2 = 3

x^2 + 1/x^2 + 2 = 3

x^2 + 1/x^2 = 3 - 2

$x^2 + \frac{1}{x^2} = 1$

$x^4 + \frac{1}{x^2} = 1$

x^4 + 1 = x^2

x^4 - x^2 + 1 = 0

Now,

Multiply both sides with (x^2 + 1), we get factorization of x^6 + 1.

(x^2 + 1)(x^4 - x^2 + 1) = 0

x^6 + 1 = 0.



Now,

Given x^206 + x^200 + x^90 + x^84 + x^18 + x^12 + x^6 + 1

= > x^200(x^6 + 1) + x^84(x^6 + 1) + x^12(x^6 + 1) + (x^6 + 1) 

= > x^200(0) + x^84(0) + x^12(0) + (0)

= > 0.



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks