SOLUTION: x=3+root8, then (x^6+x^4+x^2+1)/x^3
ans:204
shortcut formula as possible
we have to solve this in 2 minutes
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-> SOLUTION: x=3+root8, then (x^6+x^4+x^2+1)/x^3
ans:204
shortcut formula as possible
we have to solve this in 2 minutes
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Question 1042993: x=3+root8, then (x^6+x^4+x^2+1)/x^3
ans:204
shortcut formula as possible
we have to solve this in 2 minutes Answer by ikleyn(52835) (Show Source):
You can put this solution on YOUR website! .
x=3+root8, then (x^6+x^4+x^2+1)/x^3
ans:204
shortcut formula as possible
we have to solve this in 2 minutes
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1. Let us consider these two numbers: x = and y = .
It is easy to check that x*y = = = 9 - 8 = 1. (1)
Thus y = ; x and y are reciprocal.
Also notice that = = = 6. (2)
Also notice that = = = 36,
therefore = 36 - 2 = 34. (3)
Armed with this knowldge, we can make the next step.
2. Let us regroup
= + = + =
= + = ( now substitute x + y = 6, according to (2) )
= + = = 6*34 = 204. ( I substituted + = 34, according to (3) )
Answer. = 204.
Solved.
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