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If for some value of x, 5^x + 5^(–x) = B, then which of the following
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Updated on: 24 Nov 2016, 08:03
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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
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Originally posted by lalania1 on 24 Nov 2016, 07:57.
Last edited by Bunuel on 24 Nov 2016, 08:03, edited 1 time in total.
Edited the question.



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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24 Nov 2016, 07:59
Hi all,
5^–x = 5 to the x exponent. I was not able to find the right way to express it. Feel free to edit with a fix if you have it.
Looking forward to your answers on this question



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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24 Nov 2016, 08:07



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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24 Nov 2016, 09:21
lalania1 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 Let x = 1 \(5^x + 5^{–x} = \ B \ = 5 + \frac{1}{5}\) = \(\frac{26}{5}\) Let x = 2 \(5^x + 5^{–x} = 5^2 + \frac{1}{5^2}\) = 25 + \(\frac{1}{25}\) = \(\frac{626}{25}\) From the above options (A) and (B) can straightaway be rejected... (C) \(B^2 = \frac{676}{25}\) Rejected... (D) \(B^2  2 = \frac{( 676  50 )}{25}\) = \(\frac{626}{25}\) Hence, answer must be (D) \(\frac{626}{25}\)
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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25 Feb 2017, 13:16
Can someone please explain why the answer is not 5B?



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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26 Feb 2017, 03:37



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If for some value of x, 5^x + 5^(–x) = B, then which of the following
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26 Feb 2017, 07:42
Answer: D Given, 5^x + 1/ (5^x) = B Substitute 5^x = a a + 1/a = B Needed = 25^x + 25^(–x) = (5^x)^2 + 1 / (5^x)2 = a^2 +1/ a^2 = (a^4 + 1) / a^2 a + 1/a = B a^2+ 1 = a * B a^4 + 1 + 2*(a^2) = (a^2) * (B^2) [squaring both sides] a^4 + 1 = (a^2) * (B^2)  2*(a^2) (a^4 + 1) / a^2 = (B^2)  2
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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01 Dec 2017, 19:11
Can someone please advise where I went wrong?
I approached the question in the following manner:
Given: \(5^x+5^{x} = B\) Simplify: \(25^x+25^{x} = 5^{2x}+5^{2x} = 5(5^x+5^{x}) = 5(B)\)
Why can't I approach like this?



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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01 Dec 2017, 23:58



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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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23 Apr 2018, 07:32
+1 for option D. Use (a+b)^2=a^2+b^2+2ab. (5^x+5^x)^2=25^x+25^x+2=b^2 ; The required qty is b^22. Hence option D
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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24 Apr 2018, 11:31
lalania1 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 Squaring both sides of the equation, we have: [5^x + 5^(–x)]^2 = B^2 (5^2)^x + (5^2)^x + 2(5^x)(5^x) = B^2 25^x + 25^x + 2(5^0) = B^2 25^x + 25^x + 2 = B^2 25^x + 25^x = B^2  2 Answer: D
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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27 Jun 2018, 04:48
Bunuel wrote: lalania1 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 Square \(5^x + 5^{–x} = B\): \(25^{x} +2*5^x* 5^{–x}+25^{x} = B^2\); \(25^{x} +2+25^{x} = B^2\); \(25^{x} + 25^{x} = B^22\). Answer: D. Okay I had a question, but as I typed this out I got the answer... Here is a detailed step by step of Bunuel's solution. Thanks Bunuel. I was confused how he got the 2 \(* 5^x * 5^{x}\), but now I see that's just \(5^0 + 5^0\) Square \(5^x + 5^{–x} = B\) \(B^2\)= (\(5^x + 5^{x}\))(\(5^x + 5^{x}\)). Foil method... \(B^2\) = (\(5^{2x} +5^{xx} +5^{xx} +5^{2x}\)) Which then would lead to \(B^2\) = (\(5^{2x} + 5^0 + 5^0 + 5^{2x}\)) We know \(5^0\) = 1 \(B^2\) = (\(5^{2x} + 2 + 5^{2x}\)) Subtract the 2 to move it over to LHS. \(5^{2x} +5^{2x} = 25^x + 25^{x}\) \(B^2\) 2 = \(25^x + 25^{x}\)
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
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27 Jun 2018, 13:13
lalania1 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 Let x=0. \(B = 5^x + 5¯^x = 5^0 + 5^0 = 1 + 1 = 2.\) \(25^x + 25¯^x = 25^0 + 25^0 = 1 + 1 =\) \(2\). When B=2 is plugged into the answer choices, the result must be the value in blue. Only D works: \(B^2  2 = 2^2  2 = 4  2 = 2\).
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