Question

answer of this equation​

Answer 1

★GOOD NIGHT★

x² - 2x - 1 = 0

=>

x ={ 2 ±√(8)}/2

=>

x = ( 2 ± 2√2 ) /2

=>

x = ( 1 ±√2 )

=>

x² = ( 3 ±2√2 )

=>

x² - 1/x² = ( 3 ±2√2 ) - 1/(3 ±2√2)

=>

x² - 1/x² = ( 3 -2√2 ) - ( 3 + 2√2)

=>

x² -1/x² = -4√2

OR

x² - 1/x² = ( 3 + 2√2 ) - ( 3 - 2√2 )

x² - 1/x² = 4√2

NOTE:- Here, we get two values of x² - 1/x² both are correct, in their respective manners but here options are in magnitude I,e only positive quantities.

So, x² - 1/x² = 4√2