Question

what is the value of (a+1/a)^2=?​

Answer 1

Answer:

a2+1/a2+2*a *1/a

a2+1/a2

a4+1/a2

Answer 2

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

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