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01 Nov 2023, 02:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:34) correct
43%
(02:54)
wrong
based on 152
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x = 2 + √3\), what is the value of \(x^4 + \frac{1}{x^4}\)?
(A) 192
(B) 194
(C) 196
(D) 198
(E) 200
(A) 192
(B) 194
(C) 196
(D) 198
(E) 200
01 Nov 2023, 08:07
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Bunuel
OA IS B
Posted from my mobile device
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General Discussion
01 Nov 2023, 05:51
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Starting with some basic facts:
X^2+1/X^2 = [(X+1/X)^2]-2
X^4+1/X^4 = [(X^2+1/X^2)^2]-2
With this in mind:
X+1/X = :
(2+3^.5) + 1/(2+3^.5) =
[2-3^.5)/(2-3^.5)]*(2+3^.5) +1/(2+3^.5) =
1/(2-3^.5) + 1/(2+3^.5) =
(2+3^.5+2-3^.5)/1 = 4 = X+1/X
So from above,
X^2+1/X^2 = 4^2 - 2 = 14
X^4+1/X^4 = 14^2 -2 = 194
Posted from my mobile device
X^2+1/X^2 = [(X+1/X)^2]-2
X^4+1/X^4 = [(X^2+1/X^2)^2]-2
With this in mind:
X+1/X = :
(2+3^.5) + 1/(2+3^.5) =
[2-3^.5)/(2-3^.5)]*(2+3^.5) +1/(2+3^.5) =
1/(2-3^.5) + 1/(2+3^.5) =
(2+3^.5+2-3^.5)/1 = 4 = X+1/X
So from above,
X^2+1/X^2 = 4^2 - 2 = 14
X^4+1/X^4 = 14^2 -2 = 194
Posted from my mobile device
