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(1+√3+√5)^2-(√3+√5)^2=?
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18 Feb 2021, 04:23
18 Feb 2021, 04:23
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Question Stats:
89% (01:13) correct
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\((1+\sqrt{3}+\sqrt{5})^2-(\sqrt{3}+\sqrt{5})^2=\)
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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(1+√3+√5)^2-(√3+√5)^2=?
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18 Feb 2021, 06:14
18 Feb 2021, 06:14
1
Carcass wrote:
\((1+\sqrt{3}+\sqrt{5})^2-(\sqrt{3}+\sqrt{5})^2=\)
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
First recognize that (1+√3+√5)² - (√3+√5)² is a DIFFERENCE OF SQUARES.
Here are some examples of differences of squares:
x² - 25y²
4x² - 9y²
49m² - 100k²
In general, we can factor differences of squares as follows:
a² - b² = (a+b)(a-b)
So, (1+√3+√5)² - (√3+√5)² = [(1+√3+√5) + (√3+√5)][(1+√3+√5) - (√3+√5)]
= [1+2√3+2√5][1]
= 1+2√3+2√5
Answer: A
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(1+√3+√5)^2-(√3+√5)^2=?
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18 Feb 2021, 06:21
18 Feb 2021, 06:21
2
Carcass wrote:
\((1+\sqrt{3}+\sqrt{5})^2-(\sqrt{3}+\sqrt{5})^2=\)
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
A. \(1+2\sqrt{3}+2\sqrt{5} \)
B. \(1+2\sqrt{3}+3\sqrt{5} \)
C. \(1-\sqrt{3}+\sqrt{5} \)
D. \(1+\sqrt{3}-\sqrt{5} \)
E. \(\sqrt{3}+\sqrt{5}\)
\(a^2 - b^2 = (a + b)(a - b)\)
\((1+\sqrt{3}+\sqrt{5})^2-(\sqrt{3}+\sqrt{5})^2\)
\((1+\sqrt{3}+\sqrt{5}+\sqrt{3}+\sqrt{5})(1+\sqrt{3}+\sqrt{5}-\sqrt{3}-\sqrt{5})\)
\((1+2\sqrt{3}+2\sqrt{5})(1)\)
\((1+2\sqrt{3}+2\sqrt{5})\)
Hence, option A
