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woohoo921
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What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23 29 Dec 2022, 09:15
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chetan2u
What is the value of 2^x + 2^(-x) ?

\(2^x+2^{-x}=2^x+\frac{1}{2^x}\)
Square both sides..
\(2^{2x}+2^{-2x}+2=4^x+4^{-x}+2\)

(1) x < 0
Does not affect the equation at all..
Insufficient

(2) 4^x + 4^(−x) = 23
So \(4^x+4^{-x}+2=23+2=25\)
Our answer is √25=5
Sufficient

B
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chetan2u
Thank you for your helpful explanation. I do not know why I am so confused but for statement 2 I did as follows:
2^2x + 2^-2x = 23
(2^x + 2^-x)^2 = 23
Then I factored....
(2^x + 2^-x) * (2^x + 2^-x)
To get...
2^2x + 2 + (1/2^x) = 23
2^2x + (1/2^x) = 21
I did not know how to solve from here.

So two questions, Bunuel mentioned that you need to factor out the (2^x + 2^-x)^2, but it does not look like you did? Second question, if you don't have to factor out the (2^x + 2^-x)^2 to solve, just for my understanding, did I factor out correctly/how would you proceed to solve from here?

Thank you for all of your time and help.
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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23 29 Dec 2022, 20:48
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woohoo921
chetan2u
What is the value of 2^x + 2^(-x) ?

\(2^x+2^{-x}=2^x+\frac{1}{2^x}\)
Square both sides..
\(2^{2x}+2^{-2x}+2=4^x+4^{-x}+2\)

(1) x < 0
Does not affect the equation at all..
Insufficient

(2) 4^x + 4^(−x) = 23
So \(4^x+4^{-x}+2=23+2=25\)
Our answer is √25=5
Sufficient

B

chetan2u
Thank you for your helpful explanation. I do not know why I am so confused but for statement 2 I did as follows:
2^2x + 2^-2x = 23
(2^x + 2^-x)^2 = 23
Then I factored....
(2^x + 2^-x) * (2^x + 2^-x)
To get...
2^2x + 2 + (1/2^x) = 23
2^2x + (1/2^x) = 21
I did not know how to solve from here.

So two questions, Bunuel mentioned that you need to factor out the (2^x + 2^-x)^2, but it does not look like you did? Second question, if you don't have to factor out the (2^x + 2^-x)^2 to solve, just for my understanding, did I factor out correctly/how would you proceed to solve from here?

Thank you for all of your time and help.
Show more


You are wrong in the following
\(2^{2x}+2^{-2x}\). You cannot take out SQUARE from both.
\((2^{x}+2^{-x})^2= 2^{2x}+2^{-2x}+2*2^x*2^{-x}\)
So, \(2^{2x}+2^{-2x}=(2^x+2^{-x})^2-2\)
OR \(23=(2^x+2^{-x})^2-2\)
\(25=(2^x+2^{-x})^2\)
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woohoo921
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What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23 30 Dec 2022, 07:45
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chetan2u
Thank you so much for your reply. I am so sorry, but I am still confused on this step that you have below...

(2^x+2^−x)^2=2^2x + 2^−2x + 2∗ 2^x ∗ 2−x

What are you doing here then if you are not multiplying (2^x + 2^-x)*(2^x + 2^-x) out?

Thanks again!
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What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23 30 Dec 2022, 08:44
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woohoo921
chetan2u
Thank you so much for your reply. I am so sorry, but I am still confused on this step that you have below...

(2^x+2^−x)^2=2^2x + 2^−2x + 2∗ 2^x ∗ 2−x

What are you doing here then if you are not multiplying (2^x + 2^-x)*(2^x + 2^-x) out?

Thanks again!
Show more

First of all: \((a + b)^2 = a^2 + 2ab + b^2\).

Next: \(2^x+2^{−x}=2^x+\frac{1}{2^x}\).

Square the above:

    \((2^x+\frac{1}{2^x})^2=\\
    \\
    =(2^x)^2 + 2*(2^x)*(\frac{1}{2^x})+(\frac{1}{2^x})^2=\\
    \\
    =2^{2x} + 2+\frac{1}{2^{2x}}=\\
    \\
    =4^{x} + 2+\frac{1}{4^{x}}=\\
    \\
    =4^{x} + 2+4^{-x}\)

Hope it's clear.
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What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23 16 Mar 2025, 09:12
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