Find all possible solutions:
P=(x-1)*(x-2)*(x-4)*(x-8) =ax^2
Solve to get (x,y) for P(a)
Evaluate:
i. (x,y) for a=7 (original version)
ii. for a=4 (more friendly results!)
Credit: Valery Volkov
For the original version, solution from Wolfram Alpha, approximation supplied by Matlab:
>> 1/2*(sqrt(37)/2 + 15/2) + sqrt(67/8 + (15*sqrt(37))/8)
ans =
9.71818203158919
>> 1/2*(sqrt(37)/2 + 15/2) - sqrt(67/8 + (15*sqrt(37))/8)
ans =
0.82319923355992
but also complex:
1/2 (15/2 - sqrt(37)/2) + i sqrt((15 sqrt(37))/8 - 67/8)
1/2 (15/2 - sqrt(37)/2) - i sqrt(((15 sqrt(37))/8 - 67/8))
The second version was easy enough for Matlab:
eq =
(x - 1)*(x - 2)*(x - 4)*(x - 8) == 4*x^2
s =
5/2 - (7^(1/2)*1i)/2
(7^(1/2)*1i)/2 + 5/2
5 - 17^(1/2)
17^(1/2) + 5
approximations to the real solutions:
>> eval(s(3))
ans =
0.876894374382339
>> eval(s(4))
ans =
9.12310562561766
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Posted by Charlie
on 2023-04-26 22:12:20 |
computer solution
