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The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers.  Find $a+b$.

 Mar 20, 2024
 #1
avatar+128406 
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\((3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})\)

 

Product of first two

 

( 12 -sqrt 5) - 5)  =  (7 - sqrt (5) )

 

(7  -sqrt 5) ( 1+ 6sqrt 5)   =   7  + 41sqrt 5   - 30   =  -23 + 41sqrt (5)

 

cool cool cool

 Mar 20, 2024

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