prove that ( 1/2- ROOT 3)+(-2/ ROOT 5- ROOT 3) +(1/2+ ROOT 5) = 0
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Hi ,
a ) 1/ ( 2 + √3 )
= ( 2 - √3 ) / [( 2 + √3 ) ( 2 - √3 )]
= ( 2 - √3 ) / [ 4 - 3 ]
= 2 - √3 ---( 1 )
b ) 2 / ( √5 - √3 )
= 2 ( √5 + √3 ) / [ ( √5 - √3 )(√5 + √3 ) ]
= 2( √5 + √3 ) / ( 5 - 3 )
= 2 ( √5 + √3 )/ 2
= √5 + √3 ----( 2 )
c ) 1/( 2 - √5 )
= ( 2 + √5 ) / [ ( 2 - √5 ) ( 2 + √5 ) ]
= ( 2 + √5 ) / [ 4 - 5 ]
√= - ( 2 + √5 ) ---- ( 3 )
according to the problem given ,
( 1 ) + ( 2 ) + ( 3 )
= 2 - √3 + √5 + √3 - ( 2 + √5 )
= 2 - √3 + √5 + √3 - 2 - √5
= 0
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