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Help - Roots Problem

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by cmmancin » Fri Jul 08, 2011 5:42 pm
I cannot figure out the following problem for the life of me!

[√(9+(√80))+√(9-(√80))]² = ?

a. 1
b. 9 - 4√5
c. 18 - 4√5
d. 18
e. 20

Thanks in advance for any advice on how to solve this.
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by abhisays » Fri Jul 08, 2011 7:03 pm
Apply (a+b)^2 = a^2 + b^2 + 2ab

where a = [√(9+(√80))
and b = [√(9-(√80))

you will get

e.20 as answer.
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by cmmancin » Fri Jul 08, 2011 7:30 pm
I've tried using that method but am having trouble on the 2ab portion of the multiplication. Can you expand on how to multiply that portion of the equation?

Thanks!
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by abhisays » Fri Jul 08, 2011 8:23 pm
[√(9+(√80))+√(9-(√80))]²

= [√(9+(√80))² + √(9-(√80))² + 2[√(9+(√80))[√(9-(√80))
= (9+(√80) + (9-(√80) +2 (81-80)
= 18 +2 = 20
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by cmmancin » Sat Jul 09, 2011 5:45 am
Thank you!
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by Frankenstein » Sat Jul 09, 2011 7:01 am
cmmancin wrote:I cannot figure out the following problem for the life of me!

[√(9+(√80))+√(9-(√80))]² = ?

a. 1
b. 9 - 4√5
c. 18 - 4√5
d. 18
e. 20

Thanks in advance for any advice on how to solve this.
Hi,
Another method:
9+(√80) = 9 + 2√20 = 4 + 5 + 4√5 = 2^2 + (√5)^2 + 2*2*√5 = (2+√5)^2
So, √(9+(√80)) = 2 + √5
and √(9-(√80)) = √5 - 2 (because, sqrt should be positive, we consider √5 - 2 and not 2 - √5)
So, [√(9+(√80))+√(9-(√80))]² = [2 + √5 + √5 - 2]^2 = (2√5)^2 = 20
Cheers!

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