Apparently, it has three roots, but there are no easy formulas for them.
Apparently, it has three roots, but there are no easy formulas for them.
There are various numerical methods to find a solution. Once you pin one down, the other two are easy. That first on is the tricky one, but, off the top of my head, it can't be very far from zero (0). You tell me why this is so.
Shoot for x = 0.000034722222234 and see how far it gets you. Tell me how YOU managed to find it.
3 imaginary solutions:
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Guess you could "pretend" you never saw the "1"; then:
1600x(x^2 - 18) = 0
Not a bad idea! The "1" is so small compared to the other coefficients that this should give you a reasonable "first approximation". Then use a simple "perturbation method" to improve the approximation. If your first order approximation is , let to get a cubic equation in y. Make the same kind of reduction to get an approximate value, for y, then repeat with .