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(root(9 + root(80)) + root(9 - root(80)))^2 =
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15 Jun 2020, 01:26
15 Jun 2020, 01:26
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Question Stats:
72% (01:29) correct
27% (02:15) wrong based on 48 sessions
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\((\sqrt{9+\sqrt{80}}+\sqrt{9-\sqrt{80}})^2=\)
A. 1
B. \(9 - 4*\sqrt{5}\)
C. \(18 - 4*\sqrt{5}\)
D. 18
E. 20
A. 1
B. \(9 - 4*\sqrt{5}\)
C. \(18 - 4*\sqrt{5}\)
D. 18
E. 20
Re: (root(9 + root(80)) + root(9 - root(80)))^2 =
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15 Jun 2020, 01:26
15 Jun 2020, 01:26
Expert Reply
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Re: (root(9 + root(80)) + root(9 - root(80)))^2 =
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15 Jun 2020, 05:57
15 Jun 2020, 05:57
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Bookmarks
Carcass wrote:
\((\sqrt{9+\sqrt{80}}+\sqrt{9-\sqrt{80}})^2=\)
A. 1
B. \(9 - 4*\sqrt{5}\)
C. \(18 - 4*\sqrt{5}\)
D. 18
E. 20
A. 1
B. \(9 - 4*\sqrt{5}\)
C. \(18 - 4*\sqrt{5}\)
D. 18
E. 20
Notice that the expression is in the form (x + y)², where x = √(9 + √80) and y = √(9 - √80)
We know that (x + y)² = x² + 2xy + y²
If x = √(9 + √80), then x² = 9 + √80
If y = √(9 - √80), then y² = 9 - √80
Finally, xy = [√(9 + √80)][√(9 - √80)] = 81 - 80 = 1
So, we get:
(x + y)² = x² + 2xy + y²
= (9 + √80) + 2(1) + (9 - √80)
= 9 + √80 + 2 + 9 - √80
= 20
Answer: E
