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[(9+80^1/2)^1/2+(9-80^1/2)^1/2]^2 ???

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by Rahul@gurome » Sun Jul 18, 2010 3:29 pm
[(9+80^1/2)^1/2+(9-80^1/2)^1/2]^2
= [√(9 + 4√5) + √(9 - 4√5)]^2
It is of the form (a + b)^2 = a^2 + b^2 + 2ab
[√(9 + 4√5) + √(9 - 4√5)]^2 = 9 + 4√5 + 9 - 4√5 + 2√(9 + 4√5)√(9 - 4√5)
= 18 + 2√(81 - 80)
= 18 + 2 = 20

The correct answer is 20.
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