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.
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
其他解答:
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
其他解答:
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