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find a,b,c,d for all x satisfay equation
Last edited by tony123 (2007-11-03 09:21:12)
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This looks utterly dire, but by focusing on one one coefficient of x at a time, you can downgrade that to just dire.
For example, ignoring everything except x^20 terms, you get that (2x)^20 - (ax)^20 = x^20.
Equating coefficients, 2^20 - a^20 = 1.
Therefore, a = (2^20 - 1)^0.05, which is a little tidgy bit less than 2.
By ignoring everything except constant terms in a similar way, you get 1 - b^20 = d^10.
So we've already removed 2 degrees of freedom from a, b, c and d, and there are 20 more sets of coefficients to equate. If you investigate enough, you'll probably be able to find more restrictions.
(In fact, I'm guessing you'll find so many that no solutions are left, but I don't know.)
Why did the vector cross the road?
It wanted to be normal.
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