X三次方 减24倍的X平方减24等于0求X

X三次方 减24倍的X平方减24等于0求X
X三次方 减24倍的X平方减24等于0求X

X三次方 减24倍的X平方减24等于0求X
一楼结论下错了,有这样的x,可以用牛顿近似法求解,也可以用迭代法求解.
x³ - 24x² - 24 = 0
x = 24.04152286.(其他为虚数解)
用迭代法,任给x=1
x.= (24×1² + 24)^⅓ = 3.63424118.
x₁= (24×x².+ 24)^⅓ = 6.98626569.
x₂= (24×x²₁+ 24)^⅓ = 10.6129597.
x₃= (24×x²₂+ 24)^⅓ = 13.9714348.
x₄= (24×x²₃+ 24)^⅓ = 16.7611628.
x5 = (24×x²₄+ 24)^⅓ = 18.9141817.
x6 = (24×x²5 + 24)^⅓ = 20.4958631.
x7 = (24×x²6 + 24)^⅓ = 21.6201527.
x8 = (24×x²7 + 24)^⅓ = 22.4019397.
x9 = (24×x²8 + 24)^⅓ = 22.9376545.
x10 = (24×x²9 + 24)^⅓ = 23.3011830.
x11 = (24×x²10 + 24)^⅓ = 23.5462695.
x12 = (24×x²11 + 24)^⅓ = 23.7107901.
x13 = (24×x²12 + 24)^⅓ = 23.8209109.
x14 = (24×x²13 + 24)^⅓ = 23.8944784.
x15 = (24×x²14 + 24)^⅓ = 23.9435632.
x16 = (24×x²15 + 24)^⅓ = 23.9762851.
x17 = (24×x²16 + 24)^⅓ = 23.9980866.
x18 = (24×x²17 + 24)^⅓ = 24.0126067.
x19 = (24×x²18 + 24)^⅓ = 24.0222749.
x20 = (24×x²19 + 24)^⅓ = 24.0287113.
x21 = (24×x²20 + 24)^⅓ = 24.0329958.
x22 = (24×x²21 + 24)^⅓ = 24.0358476.
x23 = (24×x²22 + 24)^⅓ = 24.0377458.
x24 = (24×x²23 + 24)^⅓ = 24.0390091.
x25 = (24×x²24 + 24)^⅓ = 24.0398499.
x26 = (24×x²25 + 24)^⅓ = 24.0404094.
x27 = (24×x²26 + 24)^⅓ = 24.0407818.
x28 = (24×x²27 + 24)^⅓ = 24.0410297.
x29 = (24×x²28 + 24)^⅓ = 24.0411946.
x30 = (24×x²29 + 24)^⅓ = 24.0413044.
x31 = (24×x²30 + 24)^⅓ = 24.0413775.
x32 = (24×x²31 + 24)^⅓ = 24.0414261.
x33 = (24×x²32 + 24)^⅓ = 24.0414584.
x34 = (24×x²33 + 24)^⅓ = 24.0414800.
x35 = (24×x²34 + 24)^⅓ = 24.0414943.
x36 = (24×x²35 + 24)^⅓ = 24.0415038.
x36 = (24×x²35 + 24)^⅓ = 24.0415102.
x37 = (24×x²36 + 24)^⅓ = 24.0415144.
x38 = (24×x²37 + 24)^⅓ = 24.0415172.
x39 = (24×x²38 + 24)^⅓ = 24.0415191.
x40 = (24×x²39 + 24)^⅓ = 24.0415203.
x41 = (24×x²40 + 24)^⅓ = 24.0415212.
x42 = (24×x²41 + 24)^⅓ = 24.0415217.
x43 = (24×x²42 + 24)^⅓ = 24.0415221.
x44 = (24×x²43 + 24)^⅓ = 24.0415223.
x45 = (24×x²44 + 24)^⅓ = 24.0415225.
x46 = (24×x²45 + 24)^⅓ = 24.0415226.
x47 = (24×x²46 + 24)^⅓ = 24.0415227.
x48 = (24×x²47 + 24)^⅓ = 24.0415228.
x49 = (24×x²48 + 24)^⅓ = 24.0415228.
x50 = (24×x²49 + 24)^⅓ = 24.0415228.
x51 = (24×x²50 + 24)^⅓ = 24.0415229.
x52 = (24×x²51 + 24)^⅓ = 24.0415229.
x53 = (24×x²52 + 24)^⅓ = 24.0415229.
x54 = (24×x²53 + 24)^⅓ = 24.0415229.
x55 = (24×x²54 + 24)^⅓ = 24.0415229.
x56 = (24×x²55 + 24)^⅓ = 24.0415229.

不存在这样的X值。