Question

If a=√2+1,find the value of (a-1/a)²

Answer 1

Answer is in the picture

Hope this helps ^-^

Answer 2

Answer:

Step-by-step explanation:

Let us assume that we are asked to find the value of:

  [ (a − 1) / a] ² ;

Given: " a = √2  + 1 " ;

Substitute this value for "a" into the given expression.

Start with " (a − 1) " ;

   →  " √2 + 1 − 1 = √2 " .

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Then, the denominator is:  "a" ; so we plug in:  "√2 + 1 " ; for "a" ;

  → [ (a − 1) / a] ² ;

         =  {√2  / (√2 -1)]²

         

         =    $(\frac{\sqrt{2} }{(\sqrt{2}-1)})^{2}$  ;

Note:  Start with the "numerator" :

  " $(\sqrt{2} *\sqrt{2}) =2$ . "

Then, continue with the "denominator":

 " $(\sqrt{2} -1)^{2} = (\sqrt{2}-1)(\sqrt{2}-1)$  $= ?$ " ;

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      $(\sqrt{2} -1)^{2} = (\sqrt{2}-1)(\sqrt{2}-1)$ ;

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  →   $(\sqrt{2}-1)(\sqrt{2}-1) = ?$

  → Use the "FOIL" method (First, Outer, Inner, and Last terms, in that Order; then, combine the "like forms" to simply:

First terms: √2*√2 =  + 2 ;

Outer terms:  √2* -1 =  -1√2 ;

Inner terms:  -1 * √2  = -1√2 ;

Last terms:    -1 * -1  =  +1 ;

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Now, write these terms down in order:

 +2   -1√2  - 1√2  + 1 ;

Now, combine the "like terms:

  -1√2 - 1√2 =  - 2√2 ;

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   + 2 + 1  = 3 .

So;  we have:  - 2√2  + 3 ; for the denominator.

The answer is:  2/ (-2√3  + 3) ;  

or, write as: 2/ (3 - 2√3).

So, the answer is:  2 /