+0  
 
0
258
3
avatar+42 
Write 10+sqrt(84) in the form (a+b)^2
ricom39  Mar 15, 2012
Sort: 

3+0 Answers

 #1
avatar+42 
0
Can nobody solve this problem?
ricom39  Mar 21, 2012
 #2
avatar+3080 
0
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

12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details