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If a = 1/2-1-2, what is a2 + 2a + 4?

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If a = 1/2-1-2, what is a2 + 2a + 4?

by Max@Math Revolution » Wed Mar 04, 2020 12:18 am

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[GMAT math practice question]

If a = \(\frac{1}{\sqrt{2}-1}\) -2, what is a^2 + 2a + 4?

A. 2
B. 3
C. 4
D. 5
E. 6
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Re: If a = 1/2-1-2, what is a2 + 2a + 4?

by Max@Math Revolution » Fri Mar 06, 2020 2:00 am
=>
\(\frac{1}{\sqrt{2}-1}=\frac{\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}=\sqrt{2}+1\)

Then we have
a = √2 + 1 – 2
a = √2 - 1
or a + 1 = √2.

(a + 1)^2 = (√2)^2 = 2
a^2 + 2a + 4 = a^2 + 2a + 1 + 3 = (a + 1)^2 + 3 = 2 + 3 = 5.

Therefore, the answer is D.
Answer: D
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