Question

If a = 1 -√2, find the value of (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

Answer: √2+2

Step-by-step explanation:

1-√2-1×1+√2\1-√2×1+√2

= -1√2-√4\1-√4

=-√2-2\-1

=√2+2 Ans