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標題:

Solve for x in this question~~

發問:

X^(3/2) +12x -1=0 please show the steps as much as possible, thx.

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最佳解答:

From the equation, it seems difficult to solve it by analytical method. Instead, we should use numerical method to approximate the value of x. Let f(x) = x^3/2 + 12x - 1 f'(x) = 3/2 x^1/2 + 12 By Newton's method, The root of f(x) = 0 can be approximated by the iteration equation xn+1 = xn - f(xn)/f'(xn) With the initial guess x0 = 0, f(x0) = -1 x1 = x0 - f(x0)/f'(x0) = 0.083333333 x2 = x1 - f(x1)/f'(x1) = 0.081398463 x3 = x2 - f(x2)/f'(x2) = 0.08139807 So, corrected to 4 d.p., the root of f(x) = 0 is x = 0.0814

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