Which of the following statement is correct?

I. The value of $100^2-99^2+98^2-97^2+96^2-95^2+$ $94^2-93^2+......+2^2-1^2$ is 5050.

II. If $8 x+\frac{8}{x}=-16$ and $x<0$, then the value of $x^{197}+x^{-197}$ is 2.

Only I

Checking = $100^2-99^2+98^2-97^2+96^2-95^2+$ $94^2-93^2+......+2^2-1^2$

= (100² - 99²) + (98² - 97²) + (96² - 95²) + (94² - 93²) + ...... + (2² - 1²)

= (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + (96 - 95)(96 + 95) + (94 - 93)(94 + 93) + ...... + (2 - 1)(2 + 1)

= 1(100 + 99) + 1(98 + 97) + 1(96 + 95) + 1(94 + 93) + ...... + 1(2 + 1)

= 100 + 99 + 98 + 97 + 96 + 95 + 94 + 93 + ...... + 2 + 1

Now,

We know some n number of consecutive term = n(n + 1)/2

So, [100(100 + 1)]/2

= 50 × 101 = 5050

So, the statement I is correct

Statement II:

If 8x + 8x= -16

=  x + 1/x = - 2    [By dividing 8 from both sides]

Now, For x = - 1

x + 1/x = - 2 is satisfying

Now,

x¹⁹⁷ +  x^-197 = x¹⁹⁷ + 1/x¹⁹⁷

= (- 1)¹⁹⁷ + 1/(−1)¹⁹⁷

= - 1 – 1 = - 2

Statement II is not correct