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Solve for $a$: \(\sqrt{4+\sqrt{16+16a}}+ \sqrt{1+\sqrt{1+a}} = 6\)

michaelcai  Sep 17, 2017
 #1
avatar+87301 
+1

 

 

Note that  

 

√[ 4 +  √ [16 + 16a] ]     can be written as

 

√[ 4 +  4√ [1 + a] ]   =

 

2 √[ 1+  √ [1 + a] ]

 

Let this  = 2x

 

So we have

 

2x  + x  =  6

 

3x  = 6

 

x = 2

 

 

So...

 

√[ 1+  √ [1 + a] ]    = 2     square both sides

 

1 + √ [1 + a]  =  4          subtract 1 from both sides

 

√ [1 + a]   = 3          square both sides again

 

1 + a  =  9    →    a  =  8

 

 

cool cool cool

CPhill  Sep 18, 2017

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