If x² + 1/x² = 198, Find x² - 1/x² = ?

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04 Apr 2022 Algebra

If x² + 1/x² = 198, Find x² - 1/x² = ?

OPtion

1) 70
2) 140
3) 280
4) 70√2
5) 140√2
6) 70√5
7) 280√2
8) 140√5
9) 280√5
10) None of these

Solution

Given, x² + 1/x² = 198
(x + 1/x)² = x² + 1/x² + 2 = 198+2 = 200 ⇒ ( x + 1/x) = 10√2
(x - 1/x)² = x² + 1/x² - 2 = 198-2 = 196 ⇒ ( x - 1/x) = 14
Now, x² - 1/x² =(x + 1/x) (x - 1/x) = 10√2*14 = 140√2

Correct Option: 5 Best Solution (3)