Question

find the value of a in (a - 1/a) = 2 ​

Answer 1

Answer:

4

Step-by-step explanation:

Given,

      a = 1 - √2

⇒ a = 1 - √2

⇒ 1 / a = 1 / ( 1 - √2)

Multiplying and dividing RHS by 1 + √2 :

⇒ 1 / a = ( 1 + √2 ) / { ( 1 + √2 ) ( 1 - √2 ) }

⇒ 1 / a = ( 1 + √2 ) / { ( 1 )^2 - ( √2 )^2 }            { Using ( a + b )( a - b ) = a^2 - b^2 }

⇒ 1 / a = ( 1 + √2 ) / ( 1 - 2 )

⇒ 1 / a = ( 1 + √2 ) / ( - 1 )

⇒ 1 / a = - 1 - √2

Therefore,

⇒ a - 1 / a = 1 - √2 - ( - 1 - √2 )

⇒ a - 1 / a = 1 - √2 + 1 + √2

⇒ a - 1 / a = 2

⇒ ( a - 1 / a )^2 = 4

Answer 2

Step-by-step explanation:

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