Question

If x = 3+2√2, find the value of x^2 + 1/x^2

Answer 1

Answer:

Hi ,

x = 3 + 2√2 ---( 1 )

1/x = 1/( 3 + 2√2 )

= ( 3 - 2√2 )/[ ( 3 + 2√2 )( 3 - 2√2 )]

= ( 3 - 2√2 )/ [ 3² - ( 2√2 )² ]

= ( 3 - 2√2 ) / ( 9 - 8 )

= 3 - 2√2 ----( 2 )

x + 1/x = 3 + 2√2 + 3 - 2√2

= 6 ----( 3 )

Now ,

do the Square of equation ( 3 ) , we get

( x + 1/x )² = 6²

x² + 1/x² + 2 = 36

x² + 1/x² = 36 - 2

= 34

Answer 2

Answer:

x² + 1/x² + 2 = 36

x² + 1/x² = 36 - 2

= 34