def fd1(x):
    return 1+1/x**2

def fd2(x):
    return 1/(x-1)**0.5

# 迭代法求解方程
def Renew(x,fd,err):
    count=0
    i = 0
    try:
        while True:
            xk = fd(x)
            if abs(i) < (xk-x):
                count += 1
            else:
                count = 0
            if count > 10:
                print("不收敛")
                break
            if abs(xk-x) < err:
                return xk
            i = xk-x
            x = xk
    except Exception as e:
        print(f"发生错误: {e}")
        return None
    return None


if __name__ == "__main__":
    x0 = 1.5

    result = Renew(x0, fd1, 1e-5)
    if result is not None:
        print(f"1式收敛 解为: {result:.5f}")
    else:
        print("1式不收敛")

    result = Renew(x0, fd2, 1e-5)
    if result is not None:
        print(f"2式收敛 解为: {result:.5f}")
    else:
        print("2式不收敛")