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Source: Beat The GMAT — Quantitative Reasoning |
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neelgandham
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9+√80+9-√80+2√(81-80) = 18+2=20
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
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
