Question

If a=2-4 root 5 then find a-1/a.
help plz​

Answer 1

Answer:

Step-by-step explanation:

Given that,

a = 2 - 4√5

1 / a = 1 / ( 2 - 4√5 )

= 1 / ( 2 - 4√5 ) × ( 2 + 4√5) / ( 2 + 4√5 ) (∵Rationalising the denominator )

= 1 × ( 2 + 4√5 ) / ( 2 - 4√5) × ( 2 + 4√5 )

= ( 2 + 4√5 ) / [ ( 2 )² - ( 4√5)² ] [∵ ( a - b ) ( a + b ) = a² - b² ]

= ( 2 + 4√5 ) / [ 4 - 80 ] [ ∵ (4√5)² = ( 4)² × ( √5 )² = 16 × 5 = 80 ]

= ( 2 + 4√5 ) / ( - 76 )

= 2 ( 1 + 2√5 ) / 2 ( - 38 )

= ( 1 + 2√5 ) / ( - 38 )

∴ a - 1/a = ( 2 - 4√5 ) - [ ( 1 + 2√5 ) / ( - 38 ) ]

= ( 2 - 4√5 ) + [ ( 1 + 2√5 ) / 38 ]

= [ 38 ( 2 - 4√5 ) + 1 + 2√5 ] / 38

= [ 76 - 152√5 + 1 + 2√5 ] / 38

= [ 77 - 150√5 ] / 38 is the answer.