Question

if x=1/5+2√2 find the value of x+1/x

Answer 1

Solution :

Given x = 1/( 5 + 2√2 )

= (5 - 2√2) )/[(5+2√2)(5-2√2)]

= ( 5 - 2√2 )/[ 5² - ( 2√2 )² ]

= ( 5 - 2√2 )/( 25 - 8 )

= ( 5 - 2√2 )/17----( 1 )

=> 1/x = 5 + 2√2 ---( 2 )

Now ,

x + 1/x

= ( 5 - 2√2 )/17 + 5 + 2√2

= [ 5 - 2√2 + 17( 5 + 2√2 ) ]/17

= [ 5 - 2√2 + 85 + 34√2 ]/17

= ( 90 + 32√2 )/17

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