def f1(x):
    return 1+1/x**2

def f2(x):
    return 1/((x-1)**0.5)

def diedai(x,fd,err):
    count=0
    i = 0
    while True:
        xk = fd(x)
        if complex(xk).imag != 0:
            break
        if (i) < abs(xk-x):
            count += 1
        else:
            count = 0
        if count > 10:
            break
        if abs(xk-x) < err:
            return xk
        i = abs(xk-x)
        x = xk
    return None


if __name__ == "__main__":
    x0 = 1.5

    result = diedai(x0, f1, 1e-5)
    if result is not None:
        print(f"(1)收敛 解为: {result:.5f}")
    else:
        print("(1)不收敛")

    result = diedai(x0, f2, 1e-5)
    if result is not None:
        print(f"(2)收敛 解为: {result:.5f}")
    else:
        print("(2)不收敛")