If a = 1 + √2 , find the value of (a -1\a)root 2
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Hola there,
Given, a = 1 + √2
=> ( 1 / a ) = [ 1 / ( 1 + √2 ) ]
Multiplying and dividing by ( 1 - √2 ) :
=> ( 1 / a ) = ( 1 - √2 ) / [ ( 1 + √2 )( 1 - √2 ) ]
Use : ( x + y )( x - y ) = ( x² - y² )
=> ( 1 / a ) = ( 1 - √2 ) / [ 1² - √2² ] = ( 1 - √2 ) / [ 1 - 2 ]
= ( √2 - 1 )
Hence, ( a - 1/a ) = ( √2 + 1 ) - ( √2 - 1 ) = ( 2 )
=> ( a - 1/a )√2 = 2√2
Hope it helps...:)
Given, a = 1 + √2
=> ( 1 / a ) = [ 1 / ( 1 + √2 ) ]
Multiplying and dividing by ( 1 - √2 ) :
=> ( 1 / a ) = ( 1 - √2 ) / [ ( 1 + √2 )( 1 - √2 ) ]
Use : ( x + y )( x - y ) = ( x² - y² )
=> ( 1 / a ) = ( 1 - √2 ) / [ 1² - √2² ] = ( 1 - √2 ) / [ 1 - 2 ]
= ( √2 - 1 )
Hence, ( a - 1/a ) = ( √2 + 1 ) - ( √2 - 1 ) = ( 2 )
=> ( a - 1/a )√2 = 2√2
Hope it helps...:)
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