swerve wrote:If for some value of x, 5^x + 5^(-x) = B, then which of the following is equal to 25^x + 25^(-x)?
A) 5B
B) 5B - 10
C) B^2
D) B^2 - 2
E) B^2 - 10
The OA is D
Source: Magoosh
Let x=0.
In this case:
B = 5^x + 5^(-x) = 5^0 + 5^(-0) = 1 + 1 = 2
25^x + 25^(-x) = 25^0 + 25^(-0) = 1 + 1 = 2
Since the question stem asks for the value of 25^x + 25^(-x), the correct answer must yield 2 when B=2.
Only D works:
B^2 - 2 = 2^2 - 2 = 2
The correct answer is
D.
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