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Write 10+sqrt(84) in the form (a+b)^2
ricom39  Mar 15, 2012
 #1
avatar+42 
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Can nobody solve this problem?
ricom39  Mar 21, 2012
 #2
avatar+3077 
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ricom39:

Write 10+sqrt(84) in the form (a+b)^2



(a+b)^2 = a^2+2ab+b^2

choose a=2 then
[input]solve( (2+b)^2 = 10+sqrt(84), b )[/input]
then one suitable b is:
b=sqrt(sqrt(21)+5)*sqrt(2)-2

(a+b)^2 = ( 2 + sqrt(sqrt(21)+5)*sqrt(2)-2 )^2
admin  Mar 21, 2012
 #3
avatar+42 
0
My solution: (a+b)^2= a^2+b^2+2ab
10 + sqrt(84) = 10 + 2 (sqrt(21))
so: a^2 + b^2 = 10 and ab=sqrt(21)
solution: 7 + 3 = 10 and sqrt(7)*sqrt(3)=sqrt(21)
My answer is: (sqrt(7)+sqrt(3))^2
ricom39  Mar 22, 2012

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