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# Sorry I Couldn't Type This Out

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330
2 Thanks :D

Jan 22, 2018

#1
+1

We have

x  =       1 +   √2

_________

1 + √2

_________

1  +    .....

We can write

x  =   1  +  √2

___

x                    multiply both sides by x

x^2  =  x  +  √2

x^2  -  x   - √2   =  0

The solutions to this   are

x  =    1 /2 + √ [ 1  + 4√2]  / 2      and x  =     1/2 - √ [ 1  + 4√2]  / 2

Evaluating      1 /  [ ( x  + 1) (x - 2) ]   for either value of x gives

Here's the  detail when  x  = the first value...you can check that the other value gives exactly the same thing  for   l A l  + l B l  +  l C l

1

_________________________________________________

(  1 /2 + √ [ 1  + 4√2]  / 2   +  1)  (  1 /2 + √ [ 1  + 4√2]  / 2  - 2)

1

__________________________________________________

(  √ [ 1  + 4√2]  / 2   + 3/2 ) (   √ [ 1  + 4√2]  / 2   - 3/2 )

1

______________________

( [ 1  + 4√2]  / 4  -  9/4 )

1

_________________

√2  -   2

2  +  √2

________

-2

So  ....  A, B=  2 and C  =  -2    and    l A l  +  l B l  + l C l  =   6   Jan 22, 2018
edited by CPhill  Jan 22, 2018
#2
+2

Thank you so much! It looked so complicated haha

AnonymousConfusedGuy  Jan 22, 2018