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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Source: — Quantitative Reasoning |
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by neelgandham » Thu Nov 03, 2011 8:43 am
9+√80+9-√80+2√(81-80) = 18+2=20
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by Tani » Fri Nov 04, 2011 9:11 am
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
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