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505-555 (Easy)|   Algebra|      
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MasteringGMAT
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 06:53
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82% (01:38) correct 18% (02:33) wrong based on 865 sessions

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If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?

A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)

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gmatophobia
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 06:57
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MasteringGMAT
If a = \(\sqrt{ 2}\) — 1 and b = 1, which of the following is equal to [\(a^2\) + b(b + 2a)] + [\(b^2\) + a(a + 2b)] ?


A. 2
B. 4
C. 2\(\sqrt{ 2}\)
D. 2+2\(\sqrt{ 2}\)
E. 4+2\(\sqrt{ 2}\)
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[\(a^2\) + b(b + 2a)] + [\(b^2\) + a(a + 2b)]

\((a^2 + b^2 + 2ab) + (b^2 + a^2 + 2ab)\)

\(2(a+b)^2\)

Let's substitute the value of a and b

\(2(\sqrt{ 2} — 1+1)^2\)

\(2(\sqrt{ 2})^2\)

\(2* 2 = 4\)

Option B
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Bunuel
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 10:42
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MasteringGMAT
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)
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MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 11:28
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MasteringGMAT
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)
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\(a^2 + b(b + 2a) = a^2 + b^2 + 2ab = (a + b)^2\)

\(b^2 + a(a + 2b) = b^2 + a^2 + 2ab = (a + b)^2\)

Now, \(a + b = \sqrt{2}— 1 + 1 = 2\)

Thus, \(a + b = 2\)

Hence, \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)] = (a + b)^2 + (a + b)^2 = 2 + 2 = 4\), Answer will be (B)
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 22:50
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Bunuel
MasteringGMAT
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)

MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!
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Thanks for checking Bunuel. I may have erroneously tagged it GMATPrepNow, but It should fall under GMAT Prep. I no longer have the option to change the tag. Will you be so kind to update the tag for this question?
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 02 Jul 2023, 22:53
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Bunuel
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If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)

MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!


Thanks for checking Bunuel. I may have erroneously tagged it GMATPrepNow, but It should fall under GMAT Prep. I no longer have the option to change the tag. Will you be so kind to update the tag for this question?
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No worries. Updated the tag. :)
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 06 Oct 2024, 12:29
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Abhishek009

Your solution looks great except a+b = √2, not 2
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to 16 Oct 2025, 13:29
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