怎样解x^4-4x^3-2x^2+10x=9

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怎样解x^4-4x^3-2x^2+10x=9

怎样解x^4-4x^3-2x^2+10x=9
怎样解x^4-4x^3-2x^2+10x=9

怎样解x^4-4x^3-2x^2+10x=9
x^4-4x^3-2x^2+10x=9 (1)
只能用近似解法,如迭代法.为此:由(1)得到:
x1 = (4x0^3+2x0^2-10x0+9)^(1/4)
取初始值:x0=4 精度=0.001
解出:x1=3.9683
x1=3.9794,3.9880,3.9946,3.9997,4.0036,4.0066,4.0089,4.0108,=4.0122
4.0133,
x1=4.0141,4.0146,
小数点后第三位不再变化,方程的第一个根x近似为:x=4.014;
用类似的方法,可以求出其它的根来.

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