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Algebra .. equation

Mark Nazzal

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Use Newton's method (calculus)


Basically get an estimate/guess of X (say .2), then keep doing the iteration below (computer recommended for sanity).


Xn+1 = Xn- f(Xn)/f'(Xn)


f(x) = -4x^3+3x-1/2

f'(x) is the derivative of f(x)


Successive X's will be converge to the "real" root (they get more accurate each time), so keep doing it until it's accurate enough for you.


Here's a short cut:




Answer: x=0.17364817766693



Edit: Here's an explanation (semi-proof) why Newton's method works. Stop reading just after equation (5), we're not really interested in the rest (and it gets ugly too).

Spreading beauty with my katana.

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