Equations
This topic has expert replies
- neelgandham
- Community Manager
- Posts: 1060
- Joined: Fri May 13, 2011 6:46 am
- Location: Utrecht, The Netherlands
- Thanked: 318 times
- Followed by:52 members
9+√80+9-√80+2√(81-80) = 18+2=20
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
- Tani
- Legendary Member
- Posts: 1255
- Joined: Fri Nov 07, 2008 2:08 pm
- Location: St. Louis
- Thanked: 312 times
- Followed by:90 members
This problem becomes much simpler if you recognize that you are looking at the classic quadratic
(x+y)^2 = x^2 + 2xy + y^2.
here x^2 will equal 9 + sqrt(80)
and y^2 will equal 9 - sqrt (80)
WHen you add those the sqrt (80) terms go away and you are left with 9+9 = 18
Looking at the middle term, x*y is another classic quadratic (x+y)*(x-y) = x^2 - y^2
your product then becomes 9^2 - 80 = 1
THe answer then is 18 + 2(1) = 20
(x+y)^2 = x^2 + 2xy + y^2.
here x^2 will equal 9 + sqrt(80)
and y^2 will equal 9 - sqrt (80)
WHen you add those the sqrt (80) terms go away and you are left with 9+9 = 18
Looking at the middle term, x*y is another classic quadratic (x+y)*(x-y) = x^2 - y^2
your product then becomes 9^2 - 80 = 1
THe answer then is 18 + 2(1) = 20
Tani Wolff