Question

Simplify 1/2+root3+2/root5-root3+1/2-root5

Answer 1

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

I hope this helps you.

: )

Answer 2

Answer:

Step-by-step explanation:

1/ ( 2 + √3 )

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

= ( 2 - √3 ) / [ 4 - 3 ]

= 2 - √3 ---( 1 )

2 / ( √5 - √3 )

= 2 ( √5 + √3 ) / [ ( √5 - √3 )(√5 + √3 ) ]

= 2( √5 + √3 ) / ( 5 - 3 )

= 2 ( √5 + √3 )/ 2

= √5 + √3 ----( 2 )

1/( 2 - √5 )

= ( 2 + √5 ) / [ ( 2 - √5 ) ( 2 + √5 ) ]

= ( 2 + √5 ) / [ 4 - 5 ]

√= - ( 2 + √5 ) ---- ( 3 )

( 1 ) + ( 2 ) + ( 3 )

= 2 - √3 + √5 + √3 - ( 2 + √5 )

= 2 - √3 + √5 + √3 - 2 - √5

= 0 is the answer