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(2^2 + 2^3 + 2^4 + 2^5)/((5^(1/2) + 3^(1/2))(5^(1/2) -3^(1/2))) =
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23 Nov 2021, 04:48
23 Nov 2021, 04:48
Expert Reply
00:00
Question Stats:
100% (00:39) correct
0% (00:00) wrong based on 3 sessions
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\(\frac{2^{2} + 2^{3} + 2^{4} + 2^{5}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} =\)
A. -15
B. 0
C. 5
D. 15
E. 30
A. -15
B. 0
C. 5
D. 15
E. 30
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: (2^2 + 2^3 + 2^4 + 2^5)/((5^(1/2) + 3^(1/2))(5^(1/2) -3^(1/2))) =
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23 Nov 2021, 05:26
23 Nov 2021, 05:26
Carcass wrote:
\(\frac{2^{2} + 2^{3} + 2^{4} + 2^{5}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} =\)
A. -15
B. 0
C. 5
D. 15
E. 30
A. -15
B. 0
C. 5
D. 15
E. 30
Key property: \((a+b)(a-b) = a^2 - b^2\)
We'll apply this property to the denominator as follows:
\(\frac{2^{2} + 2^{3} + 2^{4} + 2^{5}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})} =\frac{4 + 8 + 16 + 32}{(\sqrt{5})^2 - (\sqrt{3})^2}\)
\(=\frac{60}{5-3}\)
\(=\frac{60}{2}\)
\(= 30\)
Answer: E
gmatclubot
Re: (2^2 + 2^3 + 2^4 + 2^5)/((5^(1/2) + 3^(1/2))(5^(1/2) -3^(1/2))) = [#permalink]
23 Nov 2021, 05:26
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