Question

if a =9+4√5,find √a-1/√a

Answer 1

Solution :

i ) a = 9 + 4√5

=> a = 9 + 2√(4 × 5)

=> a = 4 + 5 + 2 × √4 × √5

=> a = ( √4 )² + ( √5 )² + 2 × √4 × √5

=> a = ( √4 + √5 )²

=> √a = √4 + √5

=> √a = 2 + √5 ----( 1 )

ii ) 1/√a = 1/(2+√5 )

= ( √5 - 2 )/[(√5 + 2)(√5 - 2 )]

= (√5 - 2 )/[ (√5 )² - 2² ]

= (√5 - 2 )/( 5 - 4 )

= √5 - 2 ------( 2 )

Therefore ,

√a - 1/√a

= 2 + √5 + √5 - 2 [ from ( i ) & ( ii ) ]

= 2√5

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