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Which of following is equivalent to

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by Max@Math Revolution » Wed Apr 24, 2019 12:21 am

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question] 4.24

Which of following is equivalent to
$$\frac{\left(\sqrt{2}+1\right)^{\sqrt{3}-1}}{\left(\sqrt{2}-1\right)^{\sqrt{3}+1}}$$

A. 1
B. √2
C. 3-2√2
D. 3+2√2
E. 6√2
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by Max@Math Revolution » Fri Apr 26, 2019 5:42 am
=>
$$\frac{\left(\sqrt{2}+1\right)^{1-\sqrt{3}}}{\left(\sqrt{2}-1\right)^{1+\sqrt{3}}}=\frac{\left(\sqrt{2+1}\right)^{1-\sqrt{3}}\left(\sqrt{2}+1\right)^{1+\sqrt{3}}}{\left(\sqrt{2}-1\right)^{1+\sqrt{3}}\left(\sqrt{2}+1\right)^{1+\sqrt{3}}}=\frac{\left(\sqrt{2}+1\right)^{1-\sqrt{3}+1+\sqrt{3}}}{\left(2-1\right)^{1+\sqrt{3}}}=\left(\sqrt{2}+1\right)^{1+1}=\left(\sqrt{2}+1\right)^2=2+2\sqrt{2}+1=3+2\sqrt{2}$$

Therefore, the answer is D.
Answer: D
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