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4^x + 4 ^-x = 2 What is the value of X
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06 Mar 2021, 06:48
06 Mar 2021, 06:48
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Question Stats:
75% (01:37) correct
25% (01:14) wrong based on 32 sessions
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\(4^x + 4^{-x} = 2\) What is the value of x?
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: 4^x + 4 ^-x = 2 What is the value of X
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06 Mar 2021, 08:04
06 Mar 2021, 08:04
2
\(4^x + 4^{-x} = 2\)
\(4^x\) + \(\frac{1}{(4^x)}\) = 2
\(4^{2x} + 1 = 2 * 4^x\)
Take \(4^x\) = y, the equation will be
y^2 + 1 = 2y
\((y-1)^2\) = 0
y = 1 = \(4^x\)
So x=0
Answer C
\(4^x\) + \(\frac{1}{(4^x)}\) = 2
\(4^{2x} + 1 = 2 * 4^x\)
Take \(4^x\) = y, the equation will be
y^2 + 1 = 2y
\((y-1)^2\) = 0
y = 1 = \(4^x\)
So x=0
Answer C
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Re: 4^x + 4 ^-x = 2 What is the value of X
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06 Mar 2021, 22:15
06 Mar 2021, 22:15
1
Carcass wrote:
\(4^x + 4^{-x} = 2\) What is the value of x?
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
Solve this question in 5 seconds!
\(4^x + 4^{-x} = 2\)
\(x\) cannot be a +ve number, because it will give you a number greater than 4
\(x\) cannot be a -ve number, it will again give you a number greater than 4
\(x\) can only be zero
Anything raised to the power zero is \(1\)
Hence, option C
