plz solve.............
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Solution :
Given a = 1 - √2 ---( 1 )
1/a = 1/( 1 - √2 )
= ( 1 + √2 )/[( 1 - √2 )( 1 + √2 )]
= ( 1 + √2 )/[ 1² - ( √2 )² ]
= ( 1 + √2 )/( 1 - 2 )
= - ( 1 + √2 ) -----( 2 )
Now ,
( a - 1/a )³
= { 1 - √2 - [ -( 1 + √2 ) ] }³
= [ 1 - √2 + 1 + √2 ]³
= 2³
= 8
••••
Given a = 1 - √2 ---( 1 )
1/a = 1/( 1 - √2 )
= ( 1 + √2 )/[( 1 - √2 )( 1 + √2 )]
= ( 1 + √2 )/[ 1² - ( √2 )² ]
= ( 1 + √2 )/( 1 - 2 )
= - ( 1 + √2 ) -----( 2 )
Now ,
( a - 1/a )³
= { 1 - √2 - [ -( 1 + √2 ) ] }³
= [ 1 - √2 + 1 + √2 ]³
= 2³
= 8
••••
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